Edge-centric functional network representations of human cerebral cortex reveal overlapping system-level architecture 人类大脑皮层的边缘中心功能网络表示揭示了重叠的系统级架构
Richard F. Betzel
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Network neuroscience has relied on a node-centric network model in which cells, populations and regions are linked to one another via anatomical or functional connections. This model cannot account for interactions of edges with one another. In this study, we developed an edge-centric network model that generates constructs 'edge time series' and 'edge functional connectivity' (eFC). Using network analysis, we show that, at rest, eFC is consistent across datasets and reproducible within the same individual over multiple scan sessions. We demonstrate that clustering eFC yields communities of edges that naturally divide the brain into overlapping clusters, with regions in sensorimotor and attentional networks exhibiting the greatest levels of overlap. We show that eFC is systematically modulated by variation in sensory input. In future work, the edge-centric approach could be useful for identifying novel biomarkers of disease, characterizing individual variation and mapping the architecture of highly resolved neural circuits. 网络神经科学一直依赖于一个以节点为中心的网络模型，其中细胞、群体和区域通过解剖或功能连接相互联系。这种模型无法解释边缘之间的相互作用。在这项研究中，我们开发了一个以边缘为中心的网络模型，生成了“边缘时间序列”和“边缘功能连接”（eFC）的构建。利用网络分析，我们展示了在静息状态下，eFC 在数据集之间保持一致，并在同一人在多次扫描会话中具有可重复性。我们证明，对 eFC 进行聚类会产生将大脑自然划分为重叠簇的边缘社区，感觉运动和注意力网络中的区域展现出最高水平的重叠。我们展示了 eFC 受感觉输入变化的系统调节。在未来的工作中，以边缘为中心的方法可能有助于识别疾病的新生物标志物，描述个体差异并绘制高分辨率神经回路的结构。
N etwork science offers a promising framework for representing and modeling neural systems . From interconnected cells , to neuronal populations , to large-scale brain areas , network analysis has contributed insights into the topological principles that govern nervous system organization and shape brain function. These include small-world architecture , the emergence of integrative hubs and rich clubs , modular structure to promote specialized information processing and tradeoffs between topological features and the material and metabolic costs of wiring . 网络科学为表示和建模神经系统提供了一个有前途的框架。从相互连接的细胞，到神经元群体，再到大规模的脑区域，网络分析为理解统治神经系统组织和塑造大脑功能的拓扑原则提供了见解。这些原则包括小世界结构、整合中枢和富俱乐部的出现、模块化结构促进专门信息处理以及拓扑特征与布线的物质和代谢成本之间的权衡。
Central to these and other discoveries in network neuroscience is a simple representation of the brain in which neural elements and their pairwise interactions are treated as the nodes and edges of a network, respectively 9 . This standard model is fundamentally node-centric in that it treats neural elements (nodes) as the irreducible units of brain structure and function. This emphasis on network nodes is further reinforced by the analyses carried out on brain networks, which tend to focus on properties of nodes or groups of nodes-for example, their centralities or community affiliations . 这些以及网络神经科学中的其他发现的核心是大脑的简单表示，其中神经元元素及其成对相互作用分别被视为网络的节点和边。这种标准模型在本质上是以节点为中心的，因为它将神经元元素（节点）视为大脑结构和功能的不可简化的单位。对网络节点的强调进一步得到加强，通过对大脑网络进行的分析，这些分析往往集中在节点或节点组的属性上，例如它们的中心性或社区关联。
A limitation of the node-centric approach is that it cannot capture potentially meaningful features or patterns of inter-relationships among edges. In other scientific domains, prioritizing network edges-for example, by modeling and analyzing edge-edge interactions as a graph-has provided important insights into the organization and function of complex systems . Nonetheless, network neuroscience has remained largely focused on nodal features and partitions, paralleling a rich history of parceling, mapping and comparing cortical and subcortical gray matter regions . On the other hand, several recent studies have begun modeling brain networks from the perspective of interacting edges, including one foundational study that applied graph theoretic measures to a 'line graph'12 of interrelated white matter tracts . Although highly novel, line graphs were never adopted widely, as their construction requires users to first specify and then apply a sparsity threshold to a connectivity matrix. 节点中心方法的局限性在于它无法捕捉边之间的潜在有意义的特征或模式。在其他科学领域中，优先考虑网络边缘——例如，通过将边缘-边缘相互作用建模和分析为图形——为复杂系统的组织和功能提供了重要见解。尽管如此，网络神经科学仍然主要关注节点特征和分区，与对大脑皮层和皮下灰质区域进行分割、映射和比较的丰富历史相呼应。另一方面，最近几项研究已经开始从相互作用边缘的角度对大脑网络进行建模，其中包括一项基础研究，该研究将图论测量应用于相互关联的白质束的“线图”。尽管线图非常新颖，但由于其构建需要用户首先指定，然后将稀疏阈值应用于连接矩阵，因此从未被广泛采用。
Here we present a novel modeling framework for investigating functional brain network data from an edge-centric perspective. Our approach can be viewed as a temporal 'unwrapping' of the Pearson correlation measure-the metric commonly used for estimating the strength of functional connectivity between pairs of brain regions -thereby generating interpretable time series for each edge that express fluctuations in its weight across time. Importantly, edge time series allow the estimation of edge correlation structure, a construct we refer to as eFC. High-amplitude eFC indexes strong similarity in the co-fluctuation of two edges across time, whereas low-amplitude eFC indicates co-fluctuation patterns that are largely independent. 在这里，我们提出了一个新颖的建模框架，用于从边缘中心的角度研究功能性脑网络数据。我们的方法可以被视为对Pearson相关性测量的时间“展开” - 这是一种常用于估计脑区域间功能连接强度的度量标准 - 从而为每个边缘生成可解释的时间序列，表达其权重在时间上的波动。重要的是，边缘时间序列允许估计边缘相关结构，我们称之为eFC。高振幅的eFC指数表示两个边缘在时间上共同波动的相似性很强，而低振幅的eFC表示共同波动模式在很大程度上是独立的。
From a neuroscientific perspective, eFC can be viewed both as an extension of and a complement to traditional node-centric representations of brain networks. In node-centric network models, functional connections represent the temporal correlation of activity recorded from spatially distinct regions and often interpreted as a measure of inter-regional communication . That is, strong functional connections are thought to reflect the time-averaged strength of 'communication' between brain regions. eFC, on the other hand, tracks how communication patterns evolve over time and ultimately assesses whether similar patterns are occurring in the brain simultaneously (Supplementary Fig. 1). 从神经科学的角度来看，eFC可以被看作是对传统节点中心大脑网络表示的延伸和补充。在节点中心的网络模型中，功能连接代表了从空间上不同区域记录的活动的时间相关性，并且通常被解释为区域间通讯的一种测量。也就是说，强功能连接被认为反映了大脑区域间'通讯'的时间平均强度。另一方面，eFC跟踪了通讯模式如何随时间演变，并最终评估了大脑是否同时出现了类似的模式（见附图1）。
In this study, we demonstrate that eFC is highly replicable given sufficient amounts of data, stable within individuals across multiple scan sessions and consistent across datasets. Next, we apply data-driven clustering algorithms to , which result in partitions of the eFC network into communities of co-fluctuating edges. Each community can be mapped back to individual nodes, yielding overlapping regional community assignments. We find that brain regions associated with sensorimotor and attention networks participate in disproportionately many communities compared to other brain systems, but that, relative to one another, those same regions participate in similar sets of communities. Finally, we compare the organization of eFC at rest and during passive viewing of movies and find that eFC is consistently and reliably modulated by changes in sensory input. 在这项研究中，我们展示了在有足够数据的情况下，eFC 是高度可复制的，在多个扫描会话中在个体内是稳定的，并且在数据集之间是一致的。接下来，我们应用数据驱动的聚类算法对 进行处理，将 eFC 网络划分为共同波动边缘的社区。每个社区可以映射回个体节点，产生重叠的区域社区分配。我们发现与感觉运动和注意力网络相关的大脑区域参与了比其他大脑系统更多的社区，但相对于彼此，这些区域参与了类似的社区集合。最后，我们比较了静息状态下和 passively 观看电影期间的 eFC 组织，并发现 eFC 受感觉输入变化的影响是一致且可靠的。
Results 结果
In this section, we analyze eFC estimated using functional MRI (fMRI) data from three independently acquired datasets: 100 unrelated participants from the Human Connectome Project (HCP) , ten participants scanned ten times as part of the Midnight Scan Club (MSC) and ten participants scanned multiple times as part of the Healthy Brain Network (HBN) Serial Scanning Initiative . 在本节中，我们分析使用功能性磁共振成像（fMRI）数据估计的 eFC，这些数据来自三个独立获取的数据集：来自人类连接组计划（HCP）的 100 名无关参与者，作为午夜扫描俱乐部（MSC）的一部分被扫描了十次的十名参与者，以及作为健康大脑网络（HBN）串行扫描倡议的一部分被多次扫描的十名参与者。
eFC. Many studies have investigated networks whose nodes and edges represent brain regions and pairwise functional interactions, respectively . Here we extend this framework to consider interactions not between pairs of brain regions but between pairs of edges. eFC。许多研究已经调查了节点和边代表大脑区域和成对功能相互作用的网络。在这里，我们将这个框架扩展到考虑不是大脑区域对之间的相互作用，而是边对之间的相互作用。
Extant approaches for estimating edge-edge connectivity matrices include construction of line graphs or calculating edge overlap indices . Although suitable for sparse networks with positively weighted edges, these approaches are less appropriate for functional neuroimaging data, where networks are typically fully weighted and signed. Here we introduce a method that is well suited for these types of data, operates directly on time series and is closely related to the Pearson correlation coefficient typically used to assess strength of inter-regional functional connections. We refer to the matrices obtained using this procedure as . 现有用于估计边边连接矩阵的方法包括构建线图或计算边重叠指数。虽然适用于具有正加权边的稀疏网络，但这些方法不太适用于功能神经影像数据，因为网络通常是完全加权和带符号的。在这里，我们介绍一种适用于这些类型数据的方法，直接基于时间序列，与通常用于评估区域间功能连接强度的Pearson相关系数密切相关。我们将通过该程序获得的矩阵称为。
Beginning with regional time series, calculating eFC can be accomplished in three steps, starting by -scoring the time series (Fig. la,d). Next, for all pairs of brain regions, we calculate the element-wise product of their -scored time series (Fig. 1b,e). This results in a new set of time series, referred to as 'edge time series', whose elements represent the instantaneous co-fluctuation magnitude between pairs of brain regions and whose average across time is exactly equal to the Pearson correlation coefficient (Fig. 1c) . Co-fluctuation values are positive when activity of two regions deflects in the same direction at precisely the same moment in time, are negative when activity deflects in the opposite direction and are zero when activity is close to baseline. Importantly, the magnitude of these edge time series is not systematically related to in-scanner motion (Supplementary Fig. 2). The third and final step involves calculating the element-wise product between pairs of edge time series. When repeated over all pairs of edges, the result is an edge-by-edge matrix whose elements are normalized to the interval (Figs. If and 2a; see Methods for additional details on eFC construction). 从区域时间序列开始，可以通过三个步骤完成计算 eFC，首先是对时间序列进行评分（图1a，d）。接下来，对所有脑区域的配对，我们计算它们评分时间序列的逐元素乘积（图1b，e）。这将产生一组新的时间序列，称为“边缘时间序列”，其元素表示脑区域之间瞬时共同波动的大小，其时间平均值恰好等于皮尔逊相关系数（图1c）。当两个区域的活动在同一时刻完全朝着相同方向偏离时，共同波动值为正，当活动朝相反方向偏离时为负，当活动接近基线时为零。重要的是，这些边缘时间序列的大小与扫描中的运动没有系统关联（附图2）。第三和最后一步涉及计算边缘时间序列之间的逐元素乘积。当在所有边缘对上重复时，结果是一个边对边矩阵，其元素被归一化到区间内。 如果和 2a; 请参阅有关 eFC 构建的详细信息的方法）。
Although eFC is, to our knowledge, a novel construct, we note that the first two steps in calculating eFC are the same as those used to calculate nodal functional connectivity ( ); the mean value of any co-fluctuation time series is simply the Pearson correlation coefficient. Given that eFC is mathematically related to , we first asked whether it was possible to approximate eFC using estimates of . This is an important question. Whereas the calculation of eFC can be implemented efficiently, performing certain operations on the eFC matrix can prove computationally expensive (it is a fully weighted matrix, where , and is the number of nodes; Fig. 2b). However, a direct comparison of and is not possible owing to differences in dimensionality. Still, we can approximate eFC using nFC edge weights. Perhaps the simplest approach is to model the edge connection between region pairs and as a linear combination of the six edges that can be formed between those regions (Methods). Although this model performs poorly (correlation of observed and approximated eFC; edge-edge pairs), we can improve on its performance by including interaction terms based on node connectivity-that is, edge-edge pairs; Fig. 2c). Collectively, these observations suggest that eFC is not well approximated using linear combinations of , but, with nonlinear transformations and inclusion of interaction terms, can approximate eFC. However, these transformations are unintuitive, and the approximation still fails to fully explain variance in . 尽管据我们所知，eFC 是一种新颖的构造，但我们注意到计算 eFC 的前两个步骤与计算节点功能连接的步骤相同（ ）；任何共同波动时间序列的均值仅是皮尔逊相关系数。鉴于 eFC 在数学上与 有关，我们首先询问是否可能使用 的估计来近似 eFC。这是一个重要的问题。虽然可以有效地计算 eFC，但对 eFC 矩阵执行某些操作可能会在计算上昂贵（它是一个完全加权的 矩阵，其中 ，而 是节点数；图 2b）。然而，由于维度不同，无法直接比较 和 。尽管如此，我们可以使用 nFC 边缘权重来近似 eFC。也许最简单的方法是将区域对 和 之间的边缘连接建模为这些区域之间可以形成的六个边缘的线性组合（方法）。 尽管这个模型表现不佳（观察到的和近似的eFC之间的相关性； 边-边对），但我们可以通过包含基于节点连接性的交互项来改善其性能-也就是说， 边-边对；图2c）。总的来说，这些观察结果表明，使用线性组合无法很好地近似eFC，但是，通过非线性转换和包含交互项， 可以近似eFC。然而，这些转换是不直观的，而且近似仍然无法完全解释 中的方差。
Next, we explored variation of eFC across acquisitions and processing decisions. We found that weights are similar across three independently acquired datasets (Supplementary Fig. 3) and that the omission of global signal regression from our pre-processing pipeline induced a consistent upward shift of eFC weights, analogous to its effect on nFC (Supplementary Fig. 4). Additionally, we found that the overall pattern of eFC calculated using edge time series estimated from observed data was uncorrelated with the pattern of eFC calculated using edge time series estimated from phase-randomized surrogate time series (Supplementary Fig. 5). 接下来，我们探讨了在获取和处理决策过程中 eFC 的变化。我们发现在三个独立获取的数据集中， 权重相似（附图3），并且在我们的预处理流程中省略全局信号回归导致 eFC 权重一致上升，类似于其对 nFC 的影响（附图4）。此外，我们发现使用从观察数据估计的边缘时间序列计算的 eFC 的整体模式与使用从相位随机化替代时间序列估计的边缘时间序列计算的 eFC 模式不相关（附图5）。
Next, we asked whether eFC exhibits any clear spatial dependence, as is known to decay as a function of Euclidean distance . We assessed the spatial dispersion of eFC with the surface area of the quadrilateral formed by the centroids of the brain region pairs (we explore an alternative edge-level distance metric in Supplementary Fig. 6). We found evidence of a weak negative relationship between surface area and eFC ; edge-edge pairs; Fig. 2d), suggesting that, unlike traditional , whose connection weights are more strongly influenced by spatial relationships of brain areas to one another, eFC is less constrained by the brain's geometry. 接下来，我们询问了eFC是否表现出明显的空间依赖性，因为众所周知，它随着欧几里得距离的函数而衰减。我们通过由大脑区域对的质心形成的四边形的表面积来评估eFC的空间分散性（我们在补充图6中探索了一种替代的边级距离度量）。我们发现表面积与eFC之间存在微弱的负相关关系；边-边对；图2d），这表明，与传统的连接权重更受大脑区域之间空间关系影响的情况不同，eFC受大脑几何形状的约束较少。
Finally, we asked whether eFC bears the imprint of nFC communities-brain regions whose activity is highly correlated with members of its own community but weakly correlated or anti-correlated with members of other communities? To address this question, we classified every edge in the nFC network according to whether it fell within or between brain systems , resulting in three possible combinations of connections in the eFC graph: eFC could link edges that both fell within a community, edges that both fell between communities or an edge that fell within and an edge that fell between communities. In general, we found that eFC was significantly stronger for within-community edges compared to the other two categories (Fig. 2e). Interestingly, we found that eFC could be distinguished further by dividing within-community edges by cognitive system (one-way analysis of variance (ANOVA); ; Fig. 2f). 最后，我们询问了eFC是否带有nFC社区的印记-大脑区域的活动与其自身社区成员高度相关，但与其他社区成员弱相关或反相关？为了回答这个问题，我们根据每个nFC网络中的边是否在或者在脑系统之间进行分类，导致eFC图中三种可能的连接组合：eFC可以连接两个都在一个社区内的边，两个都在不同社区之间的边，或者一个在社区内一个在社区之间的边。总的来说，我们发现与其他两类相比，eFC对于社区内边的连接明显更强（图2e）。有趣的是，我们发现通过将社区内边按认知系统进行划分，eFC可以进一步区分（单向方差分析（ANOVA）；图2f）。
eFC is stable within individuals. In this section, we describe the robustness of eFC to scan duration - that is, how much data are required before eFC stabilizes and whether eFC is consistent across repeated scans of the same individual. To address these questions, we leveraged the within-individual design of the MSC dataset. For each participant, we aggregated their fMRI data across all scan sessions and estimated a single eFC matrix. Then, we sampled smaller amounts of temporally contiguous data, thus approximately preserving the auto-correlation structure, and estimated , which we compared against the aggregated eFC matrix (this procedure was repeated 25 times). Similarly to other studies , we found that, with small amounts of data, eFC was highly variable (Fig. 3a). However, we observed a monotonic increase in similarity as a function of time, so that, with of data, the similarity was much greater edge-edge pairs). This is of practical significance; like traditional nFC, it implies that eFC estimated using data from short scan sessions might not deliver accurate representations of an individual's edge network organization. We note that this relationship is strengthened when data are sub-sampled randomly and uniformly edgeedge pairs; Supplementary Fig. 7). eFC在个体内是稳定的。在本节中，我们描述了eFC对扫描持续时间的稳健性 - 即在eFC稳定之前需要多少数据，以及eFC在同一参与者的重复扫描中是否一致。为了回答这些问题，我们利用了MSC数据集的个体内设计。对于每个参与者，我们汇总了他们在所有扫描会话中的fMRI数据，并估计了一个单一的eFC矩阵。然后，我们对时间上连续的较小数据进行抽样，从而大致保留了自相关结构，并估计了
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Fig. 1 | Derivation of the eFC matrix. Each element of the eFC matrix is calculated based on the fMRI BOLD activity time series from four nodes (brain regions). a,d, We show four representative times series from regions , u and v. c, nFC is typically calculated by standardizing ( -scoring) each time series, performing an element-wise product (dot product) of time series pairs and calculating the average value of a product time series (actually the sum of each element divided by , where is the number of observations). To calculate eFC, we retain the vectors of element-wise products for every pair of regions. b,e, We show product time series for the pairs and , respectively. The elements of these product time series represent the magnitude of time-resolved co-fluctuation between region pairs (or edges in the nFC graph). We can calculate the magnitude of eFC by performing an element-wise multiplication of the product time series and normalizing the sum by the squared root standard deviations of both time series, ensuring that the magnitude of eFC is bounded to the interval . , The resulting value is stored in the eFC matrix. 图1 | eFC矩阵的推导。 eFC矩阵的每个元素是基于四个节点（脑区）的fMRI BOLD活动时间序列计算得出的。a、d，我们展示了来自区域 ，u和v的四个代表性时间序列。c，nFC通常通过对每个时间序列进行标准化（标准分数化），执行时间序列对的逐元素乘积（点乘）并计算产品时间序列的平均值（实际上是每个元素除以 ，其中 是观察次数）。为了计算eFC，我们保留了每对区域的逐元素乘积的向量。b、e，我们分别展示了对应于配对 和 的产品时间序列。这些产品时间序列的元素表示了区域对之间的时间相关共同波动的幅度（或nFC图中的边）。我们可以通过对产品时间序列进行逐元素乘法并将总和标准化为两个时间序列的平方根标准差来计算eFC的幅度，确保eFC的幅度被限制在间隔 内。 ，得到的值存储在 eFC 矩阵中。
Next, we examined the reliability of eFC over multiple scan sessions. That is, if we imaged an individual on separate days, would their eFC on those days be more similar to each other than to that of a different individual? We estimated eFC and calculated the pairwise similarity (Pearson correlation) between all pairs of MSC participants and scans. We found eFC to be highly reliable in the MSC dataset, where the mean within-participant similarity was compared to between participants (two-sample -test; Fig. ). Indeed, we found that, for each eFC matrix, the matrix to which it was most similar belonged to the same participant ( accuracy). Additionally, eFC exhibited slightly greater differential identifiability compared to to 0.210-calculated as the difference between mean within- and between-participant similarity . In Fig. , we show the results of applying multi-dimensional scaling to the similarity matrix from Fig. 3b. We found similar results in the HBN and HCP datasets (Supplementary Fig. 8). 接下来，我们检查了 eFC 在多次扫描会话中的可靠性。也就是说，如果我们在不同的日子对一个人进行成像，他们在那些日子的 eFC 是否更相似，而不是与另一个人的 eFC 更相似？我们估计了 eFC 并计算了所有 MSC 参与者和扫描之间的成对相似性（皮尔逊相关性）。我们发现在 MSC 数据集中，eFC 非常可靠，其中参与者内部相似性的平均值为 ，而参与者之间的相似性为 （双样本 -检验； 图 ）。事实上，我们发现，对于每个 eFC 矩阵，它最相似的矩阵属于同一参与者（ 准确度）。此外，与 相比，eFC 表现出稍微更大的差异可识别性，为 0.210 -计算为参与者内部和参与者之间相似性之间的平均差异 。在图 中，我们展示了将图 3b 中的相似性矩阵应用于多维缩放的结果。我们在 HBN 和 HCP 数据集中发现了类似的结果（附图 8）。
Collectively, these findings suggest that eFC exhibits a high level of participant specificity and captures idiosyncratic features of an individual, provided that eFC was estimated over a sufficiently long time period. This observation serves as an important validation of and suggests that eFC might be useful in future applications as substrate for biomarker generation and 'fingerprinting . 总的来说，这些发现表明，eFC 表现出高度的参与者特异性，并捕捉到个体的特异特征，前提是 eFC 是在足够长的时间段内估计的。这一观察结果是对 的重要验证，并暗示 eFC 可能在未来的应用中作为生物标志物生成和“指纹化 ”的基质有用。
The overlapping community structure of human cerebral cortex. Although many studies have investigated the brain's community structure , most have relied on methodology that forces each brain region into one and only one community. However, partitioning brain regions into non-overlapping communities clashes with evidence suggesting that cognition and behavior require contributions from regions that span multiple node-defined communities and systems . Accordingly, a definition of communities is needed that more closely matches the brain's multifunctional nature and the pervasive overlap of its community structure . 人类大脑皮层的重叠社区结构。尽管许多研究已经调查了大脑的社区结构 ，但大多数依赖于将每个脑区强制分配到一个且仅一个社区的方法。然而，将脑区划分为不重叠的社区与证据相冲突，该证据表明认知和行为需要来自跨越多个节点定义的社区和系统的区域的贡献 。因此，需要一个更符合大脑多功能性质和其社区结构普遍重叠的社区定义 。
Although deriving overlapping communities of brain regions can be challenging when using , overlap is inherent (indeed, pervasive ) within the eFC construct. Clustering the eFC matrix assigns each edge to a community. Each edge is associated with two brain regions (the nodes it connects). Thus, edge community assignments can be mapped back onto individual brain regions and, because every region is associated with edges, allow regions to simultaneously maintain a plurality of community assignments. 尽管在使用 时，推导出大脑区域的重叠社区可能具有挑战性，但在 eFC 构造中重叠是固有的（确实，是普遍的 ）。对 eFC 矩阵进行聚类将每个边分配给一个社区。每个边与两个大脑区域（它连接的节点）相关联。因此，边的社区分配可以映射回单个大脑区域，并且因为每个区域与 条边相关联，允许区域同时保持多个社区分配。
In this section, we cluster eFC matrices to discover overlapping communities in human cerebral cortex. More specifically, we use a modified -means algorithm to partition the eFC matrix into non-overlapping communities and map the edge assignments back to individual nodes. 在本节中，我们对人类大脑皮层中的 eFC 矩阵进行聚类，以发现重叠的社区。更具体地，我们使用修改后的 -means 算法将 eFC 矩阵划分为非重叠的社区，并将边的分配映射回单个节点。
In Fig. 4, we show representative communities obtained with (Supplementary Figs. 9 and 10 show examples with different numbers of communities). To demonstrate that the communities capture meaningful variance in our data, we show the edge co-fluctuation time series, the eFC matrix and the community co-assignment matrix reordered according to the derived communities (Fig. ). Here the elements of the co-assignment matrix represent the probability that two edges were assigned to the same community across partitions as we varied the number of communities from to . 在图4中，我们展示了使用 获得的代表性社区（附图9和10展示了具有不同社区数量的示例）。为了证明这些社区捕捉到了我们数据中的有意义的变化，我们展示了边缘共同波动时间序列、eFC矩阵和根据派生社区重新排序的社区共分配矩阵（图 ）。这里，共分配矩阵的元素表示两条边被分配到相同社区的概率，随着我们将社区数量从 变化到 的分区。
Fig. 2 I Organization of the eFC matrix. a, Force-directed layout of the eFC matrix (largest connected component after thresholding away weak connections). Nodes in this graph represent edges in the traditional nFC matrix. Here nodes are colored according to whether the corresponding edge fell within or between cognitive systems. Within-system edges are encircled in black. b, eFC matrix in which rows and columns correspond to pairs of brain regions. c, Two-dimensional histogram of the relationship between and the product of edges' respective weights. , Two-dimensional histogram of the relationship between eFC and the surface area of the quadrilateral defined by the four nodes. e, Mean eFC among edges where both edges fall between systems (between; ), where one edge falls within and the other between systems (mixture; ) and where both edges fall within systems (within; ). f, Mean eFC among edges within 16 cognitive systems ). All results presented in this figure are derived from HCP data. Box plots, shown in green and overlaid on data points in and , depict the interquartile range (IQR) and the median value of the distribution. Whiskers extend to the nearest points IQR above and below the 25th and 75th percentiles. Note that, in e, not all points can be displayed owing to the large number of edge-edge connections. 图2：eFC矩阵的组织。a，eFC矩阵的力导向布局（在去除弱连接后的最大连通组件）。该图中的节点代表传统nFC矩阵中的边。这里的节点根据相应边是否在认知系统内或系统间而着色。系统内边用黑色圈起。b，eFC矩阵，其中行和列对应于大脑区域对。c， 与边的 权重乘积之间关系的二维直方图。 ，eFC与由四个节点定义的四边形的表面积之间关系的二维直方图。e，两个边都在系统间（系统间； ）之间、一个边在系统内另一个在系统间（混合； ）以及两个边都在系统内（系统内； ）的边之间的平均eFC。f，16个认知系统内边的平均eFC ）。本图中所有结果均来自HCP数据。 箱线图，显示为绿色并叠加在 和 的数据点上，描述了分布的四分位距（IQR）和中位数值。须至最近的点延伸到第25和第75百分位数上下 的IQR。请注意，在e中，由于边缘连接的数量较多，无法显示所有点。
Fig. 3 | Intra- and inter-participant similarity of eFC across scan sessions. a, Correlation of session-averaged eFC matrices with eFC estimated using different amounts of data; the mean value is shown as a black line. b. Similarity of eFC within and between participants. Each block corresponds to data from a single participant; participants are also identifiable by the color of the rectangle alongside each block. c, Violin plots of within- and between-participant similarity values from the matrix shown in and within- and between-participant comparisons (two-sample -test; ). Box plots, shown in green and overlaid on data points in , depict the IQR (box) and the median value of the distribution. Whiskers extend to the nearest points IQR above and below the 25 th and 75 th percentiles. d, Scan sessions plotted according to coordinates generated by performing a two-dimensional multidimensional scaling (MDS) analysis of the matrix in b. Note that scans from the same participant (shown here with the same color) are located near each other. All panels from this figure were generated using data from the MSC. 图3 | 扫描会话中 eFC 的参与者内部和参与者间相似性。a，会话平均 eFC 矩阵与使用不同数据量估算的 eFC 的相关性；平均值显示为黑线。b，参与者内部和参与者间的 eFC 相似性。每个块对应于单个参与者的数据；参与者也可通过每个块旁边矩形的颜色进行识别。c，来自 和 矩阵的参与者内部和参与者间相似性值的小提琴图（两样本 -test； ）。绿色的箱线图叠加在 中的数据点上，描述了分布的 IQR（箱体）和中位数值。须端延伸至最近的点 IQR 在第25和第75百分位数之上和之下。d，根据在b中执行的二维多维尺度（MDS）分析生成的坐标绘制的扫描会话。请注意，来自同一参与者的扫描（此处显示为相同颜色）位于彼此附近。本图中的所有面板均使用 MSC 的数据生成。
Although the communities detected here are defined at the level of edges rather than nodes, we can project edge communities back onto brain regions. This was accomplished by extracting the edges associated with each community, determining which nodes were at the endpoints of each edge (the 'stubs') and counting the number of times that each node was represented in this stub list. We show these results in matrix form in Fig. 4d. In this panel, rows and columns represent nodes ordered according to the canonical system labels described in ref. . 尽管此处检测到的社区是在边的级别上定义的，而不是节点，但我们可以将边的社区投影回大脑区域。这是通过提取与每个社区相关联的边，确定哪些节点位于每个边的端点（'存根'）并计算每个节点在此存根列表中出现的次数来实现的。我们在图 4d 中以矩阵形式展示这些结果。在此面板中，行和列表示根据参考文献中描述的规范系统标签排序的节点。
The overlapping nature of communities is made clearer in Fig. 4e, in which communities are represented topographically. The edges associated with the same visual nodes are all involved in communities 7, 8, 9 and 10 to some extent, thereby linking the visual system to multiple other brain systems. In community 8 , for example, edges incident upon nodes in the visual and somatomotor systems are clustered together, whereas, in community 9, edges incident upon visual and control network nodes are assigned to the same community. 在图 4e 中，社区的重叠性质更加清晰，其中社区以地形方式表示。与相同视觉节点相关联的边在某种程度上都涉及到社区 7、8、9 和 10，从而将视觉系统与多个其他大脑系统连接起来。例如，在社区 8 中，涉及到视觉和体感运动系统节点的边被聚集在一起，而在社区 9 中，涉及到视觉和控制网络节点的边被分配到同一个社区。
Community overlap and functional diversity of cognitive systems. In the previous section, we showed that the human cerebral cortex could be partitioned into overlapping communities based on its edge correlation structure. This observation leads to a series of additional questions. For instance, which brain areas participate in many communities? Which participate in few? If we changed the scale of inquiry-the number of detected communities-do the answers to these questions change? Do the answers depend on which dataset we analyze? In this section, we explore these questions in detail. 认知系统的社区重叠和功能多样性。在前一节中，我们展示了人类大脑皮层可以根据其边缘相关结构被划分为重叠的社区。这一观察结果引发了一系列额外的问题。例如，哪些脑区参与了许多社区？哪些参与了少数社区？如果我们改变了调查的尺度-检测到的社区数量-这些问题的答案会改变吗？答案是否取决于我们分析的数据集？在本节中，我们将详细探讨这些问题。
One strategy for assessing community overlap is to simply count the number of different communities to which each nodes' edges are assigned . A more nuanced measure that accounts for the distribution of edge community assignments is the normalized entropy, which indexes the uniformity of a distribution. We therefore calculated normalized entropy for every brain region while varying the number of communities from to . In this section, we focus on results with . 评估社区重叠的一种策略是简单地计算每个节点的边被分配到不同社区的数量。考虑到边社区分配的分布的更微妙的度量是标准化熵，它指数了分布的均匀性。因此，我们在改变社区数量从 到 的同时，为每个脑区计算了标准化熵。在本节中，我们将重点关注 的结果。
We found that normalized community entropy was greatest within sensorimotor and attentional systems and lowest within regions traditionally associated with control and default mode networks (Fig. 5a-c). Notably, we obtained similar results from the MSC and HBN datasets (Supplementary Fig. 11), at the level of individual participants (Supplementary Fig. 12), as we varied the number of clusters (Supplementary Fig. 13) and when using different parcellation schemes (Supplementary Fig. 14). These observations seemingly contradict previous reports in which functional overlap was greatest in control networks and lowest in primary sensory systems (Fig. 5d) . 我们发现，在感觉运动和注意力系统内，标准化社区熵最高，而在传统上与控制和默认模式网络相关的区域内最低（图5a-c）。值得注意的是，我们从MSC和HBN数据集（附图11）以及个体参与者水平（附图12）获得了类似的结果，当我们改变聚类数目（附图13）和使用不同的分区方案时（附图14）。这些观察结果似乎与先前的报告相矛盾，先前的报告中功能重叠最大的是控制网络，最小的是主要感觉系统（图5d）。
Is it possible to reconcile these seemingly opposed viewpoints? To address this question, we calculated a second measure of functional diversity. Whereas normalized entropy was defined at the level of individual brain regions based on the edge communities in which they participated, this second measure was defined at the level of brain systems as a whole and assessed the average similarity of edge community assignments among the system regions (Fig. 6a,b and Methods). Intuitively, functionally diverse systems are comprised of brain regions whose edge community assignments are unique and dissimilar from one another. We found that regions within sensorimotor networks, which exhibited among the highest levels of entropy, exhibited the greatest levels of within-system similarity (Fig. 6c). In contrast, sub-networks that make up the control network exhibited the lowest levels of within-system similarity, whereas their constituent nodes had among the lowest entropy (Fig. 6c). 这些看似相反的观点是否可以调和？为了回答这个问题，我们计算了第二个功能多样性的度量。归一化熵是根据它们参与的边缘社区在个体大脑区域层面上定义的，而这第二个度量是在整个大脑系统层面上定义的，并评估了系统区域之间边缘社区分配的平均相似性（图6a、b和方法）。直觉上，功能多样性的系统由边缘社区分配独特且彼此不相似的大脑区域组成。我们发现，在感觉运动网络内的区域，熵水平最高，系统内相似性也最高（图6c）。相比之下，构成控制网络的子网络显示出最低的系统内相似性，而它们的组成节点熵水平较低（图6c）。
In the Supplementary Material, we explore the relationship of normalized entropy with more familiar measures of overlap derived from , including participation coefficient, dynamic flexibility and versatility (Supplementary Figs. 15 and 16). We also compare patterns of normalized entropy derived from eFC community structure with entropy patterns obtained using alternative methods, including line graphs, the affiliation graph model, Bayesian non-negative matrix factorization and mixed-membership stochastic block models (Supplementary Fig. 17). 在补充材料中，我们探讨了标准化熵与更熟悉的重叠度量之间的关系，这些重叠度量来自于包括参与系数、动态灵活性和多功能性在内的方法（补充图 15 和 16）。我们还比较了从 eFC 社区结构中得出的标准化熵模式与使用替代方法获得的熵模式，包括线图、从属图模型、贝叶斯非负矩阵分解和混合成员随机块模型（补充图 17）。
eFC is modulated by changes in sensory input. In the previous sections, we demonstrated that is a reliable marker of an individual and that by clustering eFC we naturally obtain overlapping communities. We leveraged this final observation to demonstrate that sensorimotor and attentional systems participate in disproportionately more communities than association cortices. Analogous to previous studies documenting the effect of task on nodal FC, we expect that eFC is also modulated by task. eFC 受感觉输入变化的调节。在前面的部分中，我们证明了 是个体的可靠标记，并且通过对 eFC 进行聚类，我们自然地获得了重叠的社区。我们利用这一最终观察结果来证明感觉运动和注意系统参与的社区比关联皮层多得多。类似于先前研究记录任务对结节 FC 的影响的研究，我们预期 eFC 也受任务调节。
To address this question, we analyzed fMRI data from the HBN Serial Scanning Initiative recorded during rest and while participants passively viewed the movie 'Raiders of the Lost Ark'. We estimated group-averaged eFC separately for each of the movie and rest scans. 为了解决这个问题，我们分析了 HBN Serial Scanning Initiative 记录的 fMRI 数据，包括休息时和参与者被动观看电影《夺宝奇兵》时的数据。我们分别估计了每个电影和休息扫描的群体平均 eFC。
In general, we found that eFC during movie watching was highly correlated with eFC estimated during rest (Fig. 7a). Across six movie 总的来说，我们发现在观看电影时的 eFC 与休息时估计的 eFC 高度相关（图 7a）。在六部电影中，
d
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Fig. 4 | Edge communities. We applied similarity-based clustering to eFC from the HCP dataset. Here we show results with the number of clusters fixed at . a, Here we reordered edge time series according to the detected community assignments. Horizontal lines divide communities from each other. The colors to the left of the time series plots identify each of the ten communities. , We also reordered the rows and columns of the eFC matrix to highlight the same ten communities. Note that, on average, within-community eFC is greater than between-community eFC. c, We calculated the probability that pairs of edges (node pairs) were co-assigned to the same community. Here we show the co-assignment matrix with rows and columns reordered according to community assignments. Note that, in general, the range of co-assignment probabilities goes to 1. Here we truncate the color limits to emphasize the ten-community partition (Supplementary Fig. 9 shows the same co-assignment matrix at different values of and with non-truncated color limits). We present two visualizations of the edge communities projected back to brain regions (nodes). d, We depict overlapping communities in matrix form. Each column in this matrix represents one of ten communities. For each community and for each node, we calculated the proportion of all edges assigned to the community that included that node as one of its endpoints ('stubs'), indicated by the color and brightness of each cell. Dark colors indicate few edges; bright colors indicate many. e, Topographic distribution of communities. Note that many of the communities resemble known intrinsic connectivity networks. However, because the communities here can overlap, it is possible for nodes associated with a particular intrinsic connectivity network to participate in multiple edge communities. 图4 | 边缘社区。我们对来自HCP数据集的eFC应用基于相似性的聚类。这里我们展示了在固定聚类数为 时的结果。a，我们根据检测到的社区分配重新排序了边缘时间序列。水平线将各个社区分开。时间序列图左侧的颜色标识了十个社区中的每一个。b，我们还重新排序了eFC矩阵的行和列，以突出相同的十个社区。请注意，平均而言，社区内的eFC大于社区间的eFC。c，我们计算了边缘对（节点对）被分配到同一社区的概率。这里我们展示了根据社区分配重新排序的共分配矩阵的行和列。请注意，一般而言，共分配概率的范围为1。这里我们截断了颜色限制以强调十个社区的划分（附图9显示了在不同值的 和未截断颜色限制下的相同共分配矩阵）。我们提供了两种将边缘社区投影回脑区域（节点）的可视化。 d, 我们以矩阵形式描绘重叠的社区。该矩阵中的每一列代表十个社区中的一个。对于每个社区和每个节点，我们计算了分配给该社区的所有边中包含该节点作为其端点之一（'stubs'）的比例，由每个单元格的颜色和亮度表示。深色表示边较少；明亮的颜色表示边较多。e, 社区的地形分布。请注意，许多社区类似于已知的内在连接网络。然而，由于这里的社区可以重叠，因此与特定内在连接网络相关联的节点可能参与多个边社区。
scans, the mean correlation with resting eFC was (all edge-edge pairs). When we compared the pairwise similarity of all movie-watching scans with rest, we found that similarity of eFC was greater within a given task than between tasks , uniform and random permutation of movie and rest conditions; Fig. 7b). To better understand what was driving this effect, we generated representative matrices for rest and movie conditions and computed the element-wise difference between these matrices. We contrasted these differences with those estimated after randomly permuting scan (condition) labels and found that of all edge connections exhibited significant changes between conditions (permutation test; ; uncorrected). Although eFC differences were widespread, the most pronounced effects were associated with two specific communities (Fig. 7c), one of which exhibited a decrease in its within-module eFC, whereas both decreased eFC with respect to each other. These communities consisted of edges associated with somatomotor and visual systems (Fig. 7d). To confirm that these system-level effects were statistically significant, we compared the mean within- and between-system eFC differences against a constrained null model in which edges communities were randomly permuted repetitions; Supplementary Fig. 18 shows a detailed schematic illustrating 扫描结果显示，与静息状态的eFC的平均相关性为 （所有 边缘对）。当我们比较所有观影扫描与静息状态之间的成对相似性时，我们发现在给定任务内的eFC相似性大于任务间的相似性 ，均匀和随机排列观影和静息条件；图7b）。为了更好地理解这一效应的驱动因素，我们生成了静息和观影条件的代表性矩阵，并计算了这些矩阵之间的逐元素差异。我们将这些差异与随机排列扫描（条件）标签后估计的差异进行对比，发现所有边缘连接中有 在条件之间出现显著变化（排列检验； ；未校正）。尽管eFC的差异普遍存在，但最显著的效应与两个特定社区相关联（图7c），其中一个社区的模内eFC减少，而两者之间的eFC均减少。这些社区包括与体感运动和视觉系统相关的边缘（图7d）。 为了确认这些系统级效应在统计上显著，我们将系统内和系统间的平均 eFC 差异与一个受限的空模型进行比较，在该模型中，边缘社区被随机置换了 次；附图。18 显示了详细的示意图
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Fig. 5 | Edge community entropy and overlap. a, Topographic distribution of normalized entropies. Normalized entropy, in this case, measures the uniformity of a node's community assignments across all communities and serves as a measure of overlap. In general, higher entropy corresponds to greater levels of overlap. b, Brain systems associated with the highest levels of normalized entropy. These include visual, attentional, somatmotor and temporoparietal systems. c, Entropy values for all brain systems; brain regions. Box plots, shown in green and overlaid on data points, depict the IQR (box) and the median value of the distribution. Whiskers extend to the nearest points IQR above and below the 25th and 75th percentiles. , Here we highlight communities in which somatomotor (red) and visual (blue) systems are represented. 图 5 | 边缘社区熵和重叠。a，标准化熵的地形分布。在这种情况下，标准化熵衡量了节点在所有社区中的分配的均匀性，并作为重叠的度量。一般来说，更高的熵对应于更高水平的重叠。b，与最高标准化熵水平相关的大脑系统。这些包括视觉、注意、体感和颞顶系统。c，所有大脑系统的熵值； 大脑区域。箱线图，显示为绿色并叠加在数据点上，描述了分布的 IQR（箱线图）和中位数值。须延伸到最近的点 IQR 在第 25 和 75 百分位数之上和之下。 ，在这里我们突出显示了体感运动（红色）和视觉（蓝色）系统被代表的社区。
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Fig. 6 | System-level similarity of edge communities. a, Edge communities can be mapped into a matrix. The element at row and column of the edge community matrix denotes the community label of edge . , We can then calculate the similarity of edge communities involving nodes and by comparing the values of columns and . This matrix depicts the similarity for all pairs of nodes. c, Within-system similarity values for each of the 16 pre-defined brain systems; within-system similarity values. Box plots, shown in green and overlaid on data points, depict the IQR (box) and the median value of the distribution. Whiskers extend to the nearest points IQR above and below the 25th and 75th percentiles. 图 6 | 边缘社区的系统级相似性。a，边缘社区可以映射到一个 矩阵中。边缘社区矩阵中第 行第 列的元素表示边缘 的社区标签。 ，然后我们可以通过比较列 和 的值来计算涉及节点 和 的边缘社区的相似性。该矩阵描述了所有节点对的相似性。c，16 个预定义脑系统中每个系统的内部相似性值； 内部相似性值。绿色显示的箱线图叠加在数据点上，显示了分布的 IQR（箱体）和中位数值。须延伸到最接近的点 IQR，超过第 25 和第 75 百分位数以下和以上的点。
this procedure). As expected, the eFC involving systems 5 and 6 was significantly decreased from rest to movie (permutation test; false discovery rate fixed at ). Supplementary Fig. 19a shows the complete list of condition differences. 此过程）。如预期的那样，涉及系统 5 和 6 的 eFC 从休息到电影时显著减少（置换检验；假发现率固定在 ）。附图 19a 显示了条件差异的完整列表。
The differences in the connection weights of eFC between movie watching and rest strongly suggested that the locations of high and low cluster overlap might also differ between conditions. To test this, we used the same clustering algorithm described earlier to partition 电影观看和休息状态之间的 eFC 连接权重差异强烈暗示高低聚类重叠位置可能在条件之间也不同。为了测试这一点，我们使用了早期描述的相同聚类算法来划分
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movie minus rest 电影减去休息
Fig. 7 | Effect of passive movie watching on eFC. a, Two-dimensional histogram of eFC estimated at rest with eFC estimated during movie watching. b, Similarity of whole-brain eFC estimated at rest with movie watching. Note that within-condition similarity is greater for both conditions. 图 7 | 被动观看电影对 eFC 的影响。a、在休息状态下估计的 eFC 与在观看电影期间估计的 eFC 的二维直方图。b、在休息状态下估计的整个大脑 eFC 与观看电影的相似性。请注意，对于两种条件，条件内相似性更大。
c, Community-averaged differences in eFC. Communities 5 and 6 are associated with the largest magnitude differences, on average. Note that these are communities estimated from HBN data and are not identical to those shown in Fig. 4, which were estimated from HCP data. d, Topographic distribution of communities 5 and 6 . Note that these communities involve edges associated with visual and somatomotor systems. e, Averaged differences in community overlap (normalized entropy); brain regions whose entropy scores were compared across rest and movie-watching conditions (permutation test; mean difference in paired samples; ). f, Similarity of whole-brain normalized entropy estimated at rest with movie watching. , Violin plot showing system-specific differences in normalized entropy. Note that some of the greatest increases in entropy are concentrated with control and default mode networks; brain regions. , Topographic distribution of differences in entropy. Box plots, shown in green and overlaid on data points in and , depict the IQR (box) and the median value of the distribution. Whiskers extend to the nearest points IQR above and below the 25th and 75th percentiles. c，社区平均的eFC差异。社区5和6平均关联着最大幅度的差异。请注意，这些社区是根据HBN数据估计的，并不完全等同于图4中显示的那些，后者是根据HCP数据估计的。d，社区5和6的地形分布。请注意，这些社区涉及与视觉和体感系统相关的边缘。e，社区重叠的平均差异（归一化熵）；对比了休息和观影条件下大脑区域的熵分数（置换检验；成对样本的平均差异；）。f，休息状态下大脑整体归一化熵与观影的相似性。小提琴图显示系统特定的归一化熵差异。请注意，一些熵增加最大的区域集中在控制和默认模式网络；大脑区域。熵差异的地形分布。箱线图，显示为绿色并叠加在和的数据点上，描述了分布的IQR（箱体）和中位数值。 胡须延伸到第25和第75百分位数上下四分位范围的最近点。
node pairs into non-overlapping clusters and, based on these clusters, calculated each node's cluster overlap as a normalized entropy. We found that, compared to rest, entropy increased during movie watching (permutation test; mean difference in paired samples; ), indicating increased overlap between communities (Fig. 7e), and that the brain-wide pattern of entropy also differed (permutation test; Fig. ). We performed analogous tests at the level of individual brain regions and found that of brain regions passed statistical testing (permutation test; false discovery rate fixed at 5%; ; Supplementary Fig. 19b). We further tested whether these differences exhibited system-specific effects by calculating the mean change in entropy for each system and comparing it against mean changes after randomly and uniformly permuting system labels. We found that seven systems exhibited such effects, with increases concentrated within control and salience/ventral attention networks and decreases in dorsal attention temporal-parietal and visual systems (permutation of system labels; false discovery rate fixed at 5%; Fig. and Supplementary Fig. 19c). 将节点对转化为不重叠的簇，并基于这些簇计算每个节点的簇重叠作为归一化熵。我们发现，与休息状态相比，在观看电影期间熵增加（排列测试；成对样本的平均差异；），表明社区之间的重叠增加（图7e），并且整个大脑的熵模式也不同（排列测试；图）。我们在个体大脑区域的水平上进行类似的测试，发现个体大脑区域中的个体通过了统计测试（排列测试；虚发现率固定在5%；；附图19b）。我们进一步测试这些差异是否表现出系统特异性效应，通过计算每个系统的熵变化均值，并将其与随机和均匀排列系统标签后的均值变化进行比较。我们发现七个系统表现出这种效应，增加集中在控制和显著性/腹侧注意网络中，而在背侧注意颞顶叶和视觉系统中减少（系统标签的排列；虚发现率固定在5%；图）。 和补充图 19c)。
Collectively, these results suggest that, like is reconfigurable and can be modulated by sensory inputs. The observed changes in eFC, which implicated two clusters associated with both somatomotor and visual systems, are in close agreement with past studies of passive movie watching that documented changes in activity and in similar . We also found increased overlap in areas associated with control and default mode networks, which agrees with evidence that activity throughout these areas is sensitive to movie narrative structure . An important area of future research involves systematically assessing the effect of different cognitively demanding tasks on eFC. 总的来说，这些结果表明，像 一样，是可重构的，并且可以通过感觉输入进行调节。观察到的 eFC 变化涉及与运动感觉和视觉系统相关的两个簇，与过去关于被动观影的研究结果高度一致，这些研究结果记录了类似 的活动和 的变化。我们还发现了与控制和默认模式网络相关的区域之间的重叠增加，这与证据一致，即这些区域的活动对电影叙事结构 敏感。未来研究的一个重要领域涉及系统评估不同认知需求任务对 eFC 的影响。
Discussion 讨论
Here we presented a network model of human cerebral cortex that focused on edge-edge interactions. The network formed by these interactions - a construct we referred to as eFC-was similar across datasets and more similar within individuals than between them. When clustered, eFC provided a natural estimate of pervasively overlapping community structure. We found that the amount of overlap varied across the cortex but peaked in sensorimotor and attention networks. We found that brain regions associated with sensorimotor and attention networks participated in disproportionately many communities compared to other brain systems, but that, relative to one another, those same regions participated in similar sets of communities. Lastly, we showed that eFC and community overlap varied systematically during passive viewing of movies. 在这里，我们提出了一个关注边缘-边缘相互作用的人类大脑皮层网络模型。这些相互作用形成的网络 - 我们称之为 eFC - 在数据集中是相似的，并且在个体内比个体间更相似。当进行聚类时，eFC 提供了广泛重叠社区结构的自然估计。我们发现重叠量在大脑皮层中有所变化，但在感觉运动和注意力网络中达到峰值。我们发现与感觉运动和注意力网络相关的大脑区域参与了比其他大脑系统更多的社区，但相对于彼此，这些区域参与了相似的社区。最后，我们展示了在观看电影时，eFC 和社区重叠在系统上有所变化。
Edge-centric perspective on functional network organization. Node-centric representations have dominated the field of network neuroscience and have served as the basis for nearly every discovery within that field . The edge-centric representation shifts focus away from dyadic relationships between nodal activations and, instead, onto the interactions between edges (similarity in patterns of co-fluctuation, a potential hallmark of communication). Although 以边缘为中心的功能网络组织视角。节点为中心的表示主导了网络神经科学领域，并成为该领域几乎每一项发现的基础。边缘为中心的表示将焦点从节点激活之间的二元关系转移到边缘之间的相互作用（共同波动模式的相似性，可能是沟通的一个标志）。尽管在其他科学领域中已经探索了相关模型，包括神经科学，在那里它们首次被用于研究交互白质，但它们需要稀疏的节点-节点连接矩阵作为输入，并且不适用于连续值时间序列数据。
related models have been explored in other scientific domains , including neuroscience, where they were first used in a study to represent interacting white matter , they require, as input, sparse node-node connectivity matrices and are poorly suited for continuous-valued time series data. 在其他科学领域中已经探索了相关模型，包括神经科学，在那里它们首次被用于研究交互白质，但它们需要稀疏的节点-节点连接矩阵作为输入，并且不适用于连续值时间序列数据。
In this study, we developed a novel edge-centric representation of functional neuroimaging data that operates directly on observed time series. Our method for estimating connection weights between edges can be viewed as a temporal 'unwrapping' of the familiar Pearson correlation-the measure frequently used to estimate the magnitude of between pairs of brain regions. Whereas the Pearson correlation coefficient calculates the time-averaged co-fluctuation magnitude for node pairs, we simply omit the averaging step, yielding 'edge time series', which represent the co-fluctuation magnitude between two nodes at every instant in time. This simple step enables us to track fluctuations in edge weight across time and, critically, allow for dyadic relationships between edges, creating an edge-centric representation of nervous system architecture (Fig. 1). If we interpret edge time series as a temporal unwrapping of , which is thought to reflect the aggregate effect of communication processes between neural element , then edge times series track, with high temporal resolution, the communication patterns between distributed neural elements. 在这项研究中，我们开发了一种新颖的功能性神经影像数据的边缘中心表示，该表示直接操作观察到的时间序列。我们估计边缘之间连接权重的方法可以被看作是对熟悉的Pearson相关性的时间“展开” - 这个测量经常用来估计大脑区域对之间关系的幅度。而Pearson相关系数计算节点对的时间平均共同波动幅度，我们简单地省略了平均步骤，得到“边缘时间序列”，它代表了在每个时间点上两个节点之间的共同波动幅度。这一简单的步骤使我们能够跟踪边缘权重在时间上的波动，并且至关重要的是，允许边缘之间的双向关系，从而创建了神经系统结构的边缘中心表示（图1）。如果我们将边缘时间序列解释为对神经元素之间通信过程的总体效果的时间展开，那么边缘时间序列可以以高时间分辨率跟踪分布式神经元素之间的通信模式。
We note that our edge-centric approach is conceptually similar to several existing methods. For instance, 'multiplication of temporal derivatives calculates the element-wise products using differenced activity time series for all pairs of nodes. These time series are then convolved with a kernel to generate smooth estimates of time-varying . Although similar, our approach relies on untransformed activity to estimate edge time series, thereby preserving the relationship between static and the mean value of each edge time series. Another related method is 'co-activation patterns' (CAPs) , which extracts and clusters voxel- or vertex-level activity during high-activity frames. Because a voxel can be co-active under different contexts, the cluster centroids spatially overlap with one another. Although both CAPs and eFC result in overlapping structures, they operate on distinct substrates, with CAPs focusing on activity and eFC focusing on similarity of co-activity. Although CAPs requires the specification of additional parameters compared to eFC-for example, the threshold for a high-activity frameCAPs might scale better owing to the focus on activity rather than connectivity. 我们注意到我们的边缘中心方法在概念上与几种现有方法类似。例如，“时间导数的乘法”通过使用节点对的差异活动时间序列计算元素级乘积。然后，这些时间序列与核卷积以生成时间变化的平滑估计。尽管类似，我们的方法依赖于未转换的活动来估计边缘时间序列，从而保留静态关系和每个边缘时间序列的均值之间的关系。另一个相关方法是“共同激活模式”（CAPs），它在高活动帧期间提取和聚类体素或顶点级活动。由于一个体素可以在不同情境下共同激活，聚类中心在空间上会相互重叠。尽管CAPs和eFC都会产生重叠结构，但它们作用于不同的基质，CAPs关注活动，而eFC关注共同激活的相似性。 尽管 CAPs 需要相对于 eFC 指定额外的参数，例如，高活动帧的阈值，但由于其专注于活动而不是连接性，CAPs 可能更好地扩展。
Finally, we note that and are both frameworks for investigating pairwise relationships from neural time series. Critically, however, and eFC differ in terms of what elements are being related to one another and how we interpret those relationships. In the case of , correlations refer to similarities in the activity of individual neural elements, often interpreted as two parts of the brain 'talking' to one another. In the case of eFC, on the other hand, correlations express similarities in co-fluctuations along edges, which might loosely be interpreted as 'conversations' between node pairs (Supplementary Fig. 1). In other words, nFC focuses on co-activation between nodes whereas focuses on co-fluctuation along edges. In this way, and should be viewed as complementary approaches that can reveal unique organizational features of nervous systems. 最后，我们注意到 和 都是用于研究神经时间序列中成对关系的框架。然而，关键在于， 和 eFC 在被关联的元素以及我们如何解释这些关系方面存在差异。在 的情况下，相关性指的是个别神经元活动的相似性，通常被解释为大脑的两个部分在“交流”。另一方面，在 eFC 的情况下，相关性表示边缘上的共同波动的相似性，这可能被宽泛解释为节点对之间的“对话”（附图 1）。换句话说，nFC 关注节点之间的共同激活，而 关注边缘上的共同波动。通过这种方式， 和 应被视为可以揭示神经系统独特组织特征的互补方法。
Overlapping communities extend understanding of system-level cortical organization. Here we demonstrated that clustering eFC using community detection methods naturally leads to communities that overlap when mapped back to the level of brain regions and nodes. Past investigations of cortical organization have focused almost exclusively on non-overlapping communities. The decision to define communities in this way is partially motivated by interpretability but also by limitations of the methods used to detect communities, which assign nodes to one community only . This current view of communities has been profoundly successful'. It provides a low-dimensional description of the brain, it can be used to define node roles and detect hubs , and it can be applied to both anatomical and functional networks with equal success. 重叠的社区扩展了对系统级皮层组织的理解。在这里，我们展示了使用社区检测方法对eFC进行聚类自然地导致了在映射回脑区和节点级别时重叠的社区。过去对皮层组织的研究几乎完全集中在非重叠的社区上。以这种方式定义社区的决定部分受可解释性的驱动，但也受到用于检测社区的方法的限制的影响，这些方法仅将节点分配给一个社区。当前对社区的这种观点取得了巨大成功。它提供了对大脑的低维描述，可以用来定义节点角色和检测中心，可以在解剖和功能网络上同样成功地应用。
The dominant non-overlapping perspective of communities has strongly influenced how we think about brain function. Because functional communities exhibit reliable correspondence with patterns of task-evoked activity , we have come to associate individual communities with specific cognitive domains. For instance, it is not uncommon to refer to communities as primarily processing visual information, enacting cognitive control or performing attentional functions. This localization of brain function to communities, although likely a reasonable first-order approximation, perpetuates a view of brain function in which brain areas, systems and communities are fundamentally unifunctional. Such a view, however, disagrees with observations that many aspects of cognition and behavior transcend these traditional community labels. 社区的主导非重叠视角强烈影响了我们对大脑功能的思考。由于功能性社区与任务诱发活动的模式呈现可靠的对应关系，我们开始将个体社区与特定的认知领域联系起来。例如，将社区主要视为处理视觉信息、执行认知控制或执行注意功能并不罕见。尽管将大脑功能定位于社区可能是一个合理的一阶近似，但这种观点延续了一个大脑功能的观点，即大脑区域、系统和社区基本上是单一功能的。然而，这种观点与许多认知和行为方面超越这些传统社区标签的观察不符。
Another perspective is that overlap arises from time-varying fluctuations in community structure . That is, at any given instant, communities are non-overlapping but appear 'fuzzy' due to nodes changing their community allegiances over time. The approach developed here is closely aligned with the perspective that brain areas and communities are dynamic and exhibit highly degenerate functionality. Other studies have investigated overlapping and dynamic communities by studying overlap in co-activation or through the use of sliding window analysis and multi-layer models to detect flexible regions that change their community assignment over time. Our approach, however, is distinct, emphasizing a state of pervasive overlap in which nodes belong to several communities instantaneously. 另一个观点是，重叠是由社区结构中随时间变化的波动引起的。也就是说，在任何给定时刻，社区是不重叠的，但由于节点随时间改变其社区归属，它们看起来“模糊”。这里开发的方法与大脑区域和社区是动态的、表现出高度退化功能的观点密切相关。其他研究通过研究共同激活中的重叠或通过使用滑动窗口分析和多层模型来探究重叠和动态社区，以检测随时间改变其社区分配的灵活区域。然而，我们的方法是独特的，强调一种普遍重叠状态，即节点瞬间属于多个社区。
Limitations. One of the most important limitations concerns the estimation of edge time series from functional imaging data. To calculate edge time series, we first -scored regional time series. Here, the -score is appropriate only if the time series has a temporally invariant mean and s.d. If there is a sustained increase or decrease in activity-for example, the effect of a blocked taskthen the -scoring procedure can result in a biased mean and s.d., resulting in poor estimates of fluctuations in activity. In future work, investigation of task-evoked changes in eFC could be investigated with already common pre-processing steps-for example, constructing task regressors to remove the first-order effect of tasks on activity . 限制。其中一个最重要的限制涉及从功能成像数据中估计边缘时间序列。为了计算边缘时间序列，我们首先对区域时间序列进行了 -score。在这里， -score 只有在时间序列具有时间不变的均值和标准差时才是合适的。如果活动有持续增加或减少的情况-例如，受阻任务的影响-那么 -score 过程可能导致偏倚的均值和标准差，从而导致对活动波动的估计不准确。在未来的工作中，可以通过已经常见的预处理步骤来研究任务诱发的eFC变化-例如，构建任务回归器以消除任务对活动的一阶影响 。
Another limitation concerns the scalability of eFC. Calculating eFC given for a brain divided into parcels results in an matrix of dimensions . This means that an increase in the number of parcels results in a squared increase in the dimensionality of eFC. If the number of parcels is large, this can result in massive, fully weighted matrices that require large amounts of memory to store and manipulate. In the future, however, it might be necessary to explore dimension reduction methods to retain the most relevant sub-graphs for a given task or set of behaviors. 另一个限制涉及 eFC 的可扩展性。计算将大脑划分为 个区块的 eFC 会导致一个 维度为 的矩阵。这意味着区块数量的增加会导致 eFC 维度的平方增加。如果区块数量很大，这可能导致需要大量内存来存储和操作的大型、完全加权的矩阵。然而，未来可能需要探索降维方法，以保留给定任务或行为集的最相关子图。
Future directions. Although eFC characterizes interactions between edges rather than nodes, it can still be analyzed using the same methods previously applied to . We can use graph theory to detect its hubs and communities (Supplementary Fig. 20 shows examples), estimate edge gradients and compare eFC connection weights across individuals and conditions . On the other hand, eFC affords many new opportunities, beginning with the edge time series used to estimate eFC. Essentially, edge time series offer a moment-to-moment assessment of how strongly two nodes (brain regions) co-fluctuate with one another, providing an estimate of time-varying without the requirement that we specify a window . This overcomes one of the main limitations of sliding window estimates of time-varying , namely that the use of a 未来的方向。虽然 eFC 描述的是边之间的相互作用，而不是节点，但仍然可以使用之前应用于 的相同方法进行分析。我们可以使用图论来检测其中心和社区 （附图 20 显示示例），估计边缘梯度 并比较个体 和条件 下的 eFC 连接权重。另一方面，eFC 提供了许多新机会，从用于估计 eFC 的边缘时间序列开始。基本上，边缘时间序列提供了两个节点（脑区域）如何随时间共同波动的瞬时评估，提供了时间变化的估计 ，而无需指定窗口 。这克服了滑动窗口估计时间变化的 的主要限制之一，即使用窗口的需求。
window leads to a 'blurring' of events across time 42 . Other directions for future work include developing whole-brain functional atlases with overlapping system labels and applications to specific brain areas and sub-systems for constructing fine-grained overlapping atlases . We note, also, that, because the derivation of eFC is based on Pearson correlations, it would be straightforward to estimate analogs of eFC based on lagged and partial relationships. 窗口导致时间上事件的“模糊”42。未来工作的其他方向包括开发具有重叠系统标签的整个脑功能图谱，以及应用于特定脑区域和子系统以构建细粒度重叠图谱。我们还注意到，由于eFC的推导基于Pearson相关性，因此可以直接估计基于滞后和部分关系的eFC的类似物。
eFC might be useful in applications of machine learning and classification of neuroimaging data . The dimensionality of the eFC matrix is much greater than that of a typical nFC matrix. We speculate that some of the added dimensions might be useful for studying brain-behavior relationships-for example, by identifying manifolds along which individuals, clinical cohorts or behaviors naturally separate, enhancing classification accuracy (the results of exploratory analyses of brain-behavior relationships based on eFC are shown in Supplementary Figs. 21-23). On the other hand, the increased dimensionality of eFC requires special considerations, as it presents statistical and interpretational challenges. Multivariate methods , such as canonical correlation analysis or partial least squares, both of which can help circumvent multiple comparison issues, might prove useful and should be investigated in future brain-behavior analysis involving eFC. eFC可能在机器学习和神经影像数据分类应用中很有用。eFC矩阵的维度远远大于典型的nFC矩阵。我们推测，一些额外的维度可能有助于研究大脑行为关系，例如通过识别沿着个体、临床队列或行为自然分离的流形，增强分类准确性（基于eFC的大脑行为关系的探索性分析结果见附录图21-23）。另一方面，eFC的增加维度需要特别考虑，因为它带来了统计和解释上的挑战。多变量方法，如典型相关分析或偏最小二乘法，都可以帮助规避多重比较问题，可能会在未来涉及eFC的大脑行为分析中证明有用，并应该进行研究。
Additionally, future studies should investigate appropriate null models for eFC. Like nFC, eFC is correlation based, and the weights of edge-edge connections are not independent of one another . This means that rewiring-based null models (which treat connections as independent) are not appropriate. Consideration should be given to other classes of null models, including time-series-based surrogates. Appropriate null models might help clarify brainbehavior relationships in future studies. 此外，未来的研究应该探讨适用于eFC的空模型。与nFC一样，eFC是基于相关性的，边-边连接的权重彼此不独立。这意味着基于重连的空模型（将连接视为独立的）并不适用。应考虑其他类别的空模型，包括基于时间序列的替代物。适当的空模型可能有助于澄清未来研究中的脑行为关系。
The framework proposed here for investigating interactions between pairs of nodes can be generalized to study mutual interactions between many more nodes by simply calculating the element-wise product of node triplets, quartets and quintets . This extension is, in some respects, analogous to recent applications of algebraic topology , which can uncover higher-order relationships in a network (through graph simplices). We note, however, that, although generating higher-order time series is straightforward, it is necessarily accompanied by an increase in dimensionality, potentially making the approach computationally intractable for whole-brain networks. On the other hand, higher-order time series (and their corresponding eFC analogs) might be useful for investigating the organization of predefined circuits composed of relatively few brain regions or nuclei. 这里提出的用于研究节点对之间相互作用的框架可以推广到通过简单计算节点三元组、四元组和五元组的元素乘积来研究更多节点之间的相互作用。在某些方面，这种扩展类似于最近代数拓扑的应用，可以揭示网络中的高阶关系（通过图单纯形）。然而，需要注意的是，尽管生成高阶时间序列很简单，但必然会伴随着维度的增加，这可能使得这种方法在整个大脑网络中计算上变得棘手。另一方面，高阶时间序列（及其对应的eFC模拟）可能有助于研究由相对较少的脑区或核团组成的预定义电路的组织。
Lastly, the edge-centric framework developed here is not limited to fMRI and can be easily extended to different recording modalities, including scalp/intracranial electroencephalography or magnetoencephalography, which makes it possible to track seizure propagation at the level of . Similarly, the application of this approach to datasets resolving single-neuron activity could uncover important connection-level insights into circuit organization . 最后，在这里开发的以边缘为中心的框架不仅限于 fMRI，而且可以轻松扩展到不同的记录模式，包括头皮/颅内脑电图或脑磁图，这使得可以在 级别跟踪癫痫传播。同样，将这种方法应用于解析单个神经元活动的数据集可能揭示有关电路组织的重要连接级见解 。
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Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41593-020-00719-y. 任何方法、额外参考资料、自然研究报告摘要、源数据、扩展数据、补充信息、致谢、同行评审信息；作者贡献和竞争利益的详细信息；以及数据和代码可用性声明均可在 https://doi.org/10.1038/s41593-020-00719-y 获取。
Received: 9 September 2019; Accepted: 3 September 2020; 收到日期：2019 年 9 月 9 日；接受日期：2020 年 9 月 3 日；
Published online: 19 October 2020 在线发表日期：2020 年 10 月 19 日
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Methods 方法
In this study, we used data from three independently acquired, openly available neuroimaging datasets and, therefore, did not collect any data for this study. No statistical methods were used to pre-determine sample sizes, but our sample sizes are similar to those reported in previous publications , and represent either all usable data (MSC and HBN) or a subset pre-selected by the study coordinators (HCP). We did not perform any randomization of participants into experimental groups, and we opted to analyze each dataset separately. Appropriate counterbalancing of task conditions was performed by the authors of the original studies . Data analysis was not performed blinded to the conditions of the experiments. Blinding was not relevant because participants were not evaluated based on group membership, and blinding is not applicable to the whole-group analyses reported in this study. All analyses were performed with MATLAB (MathWorks, Inc.) version 2019a. Further study design and statistical details can be found in the Life Sciences Reporting Summary available online. 在这项研究中，我们使用了三个独立获取的、公开可用的神经影像数据集，并且没有为这项研究收集任何数据。我们没有使用统计方法来预先确定样本量，但我们的样本量与先前发表的研究报告中的相似，并且代表了所有可用数据（MSC和HBN）或由研究协调员预先选择的子集（HCP）。我们没有将参与者随机分配到实验组中，而是选择分别分析每个数据集。原始研究的作者进行了适当的任务条件平衡。数据分析没有在对实验条件不知情的情况下进行。由于参与者不是根据组别成员身份进行评估，因此盲法不适用于本研究中报告的整体组分析。所有分析均使用MATLAB（MathWorks，Inc.）2019a版本进行。更多研究设计和统计细节可在在线提供的生命科学报告摘要中找到。
Datasets. The HCP dataset included resting state functional magnetic resonance imaging (rsfMRI) data from 100 unrelated adult participants (54% female; mean age years; age range, years). These participants were selected as they comprised the ' 100 Unrelated Subjects' released by the HCP. The study was approved by the Washington University Institutional Review Board, and informed consent was obtained from all participants. Participants underwent four 15-min rsfMRI scans over a 2-day period. A full description of the imaging parameters and image pre-processing can be found in ref. . The rsfMRI data were acquired with a gradient-echo echo-planar imaging (EPI) sequence (run duration , , flip angle isotropic voxel resolution, multi-band factor ) with eyes open and instructions to fixate on a cross. Images were collected on a 3T Siemens Connectome Skyra with a 32-channel head coil. 数据集。HCP数据集包括来自100名无关成年参与者的静息态功能磁共振成像（rsfMRI）数据（54%女性；平均年龄岁；年龄范围岁）。这些参与者被选为HCP发布的“100名无关主体”之一。该研究获得了华盛顿大学机构审查委员会的批准，并从所有参与者那里获得了知情同意。参与者在两天内接受了四次15分钟的rsfMRI扫描。有关成像参数和图像预处理的详细描述可在参考文献中找到。rsfMRI数据采用了梯度回波回波成像（EPI）序列（运行持续时间、翻转角度、等向性像素分辨率、多带因子）进行获取，眼睛睁开并接收到盯着十字架的指令。图像是在一台3T西门子Connectome Skyra上使用32通道头线圈收集的。
The MSC dataset included rsfMRI from 10 adults ( female; mean age years; age range, years). The study was approved by the Washington University School of Medicine Human Studies Committee and Institutional Review Board, and informed consent was obtained from all participants. Participants underwent 12 scanning sessions on separate days, each session beginning at 24:00. Ten rsfMRI scans per participant were collected with a gradient-echo EPI sequence (run duration , flip angle isotropic voxel resolution) with eyes open and with eye tracking recording to monitor for prolonged eye closure (to assess drowsiness). Images were collected on a 3T Siemens Trio. MSC数据集包括了来自10名成年人的静息态功能磁共振成像（其中 为女性；平均年龄 岁；年龄范围 岁）。该研究已获得华盛顿大学医学院人类研究委员会和机构审查委员会的批准，并已获得所有参与者的知情同意。参与者在不同的日子里进行了12次扫描会话，每次会话从24:00开始。每位参与者进行了10次静息态功能磁共振成像扫描，采用了梯度回波EPI序列（运行持续时间 ，翻转角度 各向同性像素分辨率），眼睛睁开并进行眼动追踪记录以监测是否有长时间闭眼（以评估嗜睡）。图像采集于3T西门子Trio。
The HBN Serial Scanning Initiative dataset included rsfMRI and movie-watching functional magnetic resonance imaging (mvfMRI) from 13 adults ( female; mean age years; age range, years). Three participants of the HBN dataset did not have enough non-outlier functional scans (see quality control criteria below) to be meaningfully analyzed (non-outlier scan percentage and ) and were excluded entirely from the current study. This rendered the HBN dataset as ten participants ( female; mean age years; age range, years). The study was approved by the Chesapeake Institutional Review Board, and informed consent was obtained from all participants. Participants underwent 14 scanning sessions over a 1-2-month period, in which runs were acquired per participant. On the eighth session, participants viewed the movie 'Raiders of the Lost Ark' (Lucasfilm) in six approximately 20 -min scans. The rsfMRI and mvfMRI were acquired with a gradient-echo EPI sequence (run duration per segment, run duration per segment, , flip angle voxel resolution, multi-band factor with participants instructed to keep their eyes open and gaze directed toward a cross during the fsMRI scan. Images were collected on a 1.5T Siemens Avanto with a 32-channel head coil. The mvfMRI was divided into six successive scan sessions, which we further truncated by retaining the first 420 samples so that the duration matched that of the HBN rsfMRI, of which we retained the first six for the sake of balance. HBN串行扫描计划数据集包括来自13名成年人的静息态功能磁共振成像（rsfMRI）和观看电影的功能磁共振成像（mvfMRI）（其中女性；平均年龄岁；年龄范围岁）。HBN数据集中有三名参与者没有足够的非异常功能扫描（请参见下面的质量控制标准）可进行有意义的分析（非异常扫描百分比和），因此完全被排除在当前研究之外。这使得HBN数据集中只有十名参与者（女性；平均年龄岁；年龄范围岁）。该研究已获得切萨皮克机构审查委员会的批准，并从所有参与者那里获得知情同意。参与者在一个1-2个月的时间内进行了14次扫描会话，每位参与者获得次扫描。在第八次会话中，参与者观看了电影《夺宝奇兵》（卢卡斯影业）的六个约20分钟的扫描。 rsfMRI和mvfMRI采用梯度回波EPI序列获取（每段运行时间 ，每段运行时间 ， ，翻转角度 像素分辨率，多带因子 ，参与者被指示在fsMRI扫描期间保持眼睛睁开并注视十字。图像是在1.5T西门子Avanto上采集的，使用32通道头线圈。mvfMRI被分为六个连续的扫描会话，我们进一步截取了前420个样本，以使其持续时间与HBN rsfMRI相匹配，我们保留了前六个样本以保持平衡。
Image pre-processing. HCP functional pre-processing. Functional images in the HCP dataset were minimally pre-processed according to the description provided in ref. . Briefly, these data were corrected for gradient distortion, susceptibility distortion and motion and then aligned to a corresponding T1-weighted (T1w) image with one spline interpolation step. This volume was further corrected for intensity bias and normalized to a mean of 10,000 . This volume was then projected to the _fs_LR mesh, excluding outliers, and aligned to a common space using a multi-modal surface registration . The resultant CIFTI file for each HCP individual who participated in this study followed the file naming pattern LR,RL _Atlas_MSMAll.dtseries.nii. 图像预处理。HCP功能预处理。根据参考文献提供的描述，HCP数据集中的功能图像进行了最小预处理。简而言之，这些数据经过了梯度失真、磁化失真和运动的校正，然后与相应的T1加权（T1w）图像对齐，使用一次样条插值步骤。这个体积进一步校正了强度偏差，并标准化为平均值10,000。然后将这个体积投影到 _fs_LR网格上，排除异常值，并使用多模式表面配准对齐到一个公共空间。参与本研究的每个HCP个体的结果CIFTI文件遵循文件命名模式 LR,RL _Atlas_MSMAll.dtseries.nii。
MSC and HBN functional pre-processing. Functional images in the MSC and HBN datasets were pre-processed using fMRIPrep 1.3.2 (ref. ), which is based on Nipype 1.1.9 (ref. ). The following description of fMRIPrep's pre-processing is based on boilerplate distributed with the software covered by a 'no rights reserved' (CC0) license. Internal operations of fMRIPrep use Nilearn 0.5.0 (ref. ), ANTs 2.2.0, FreeSurfer 6.0.1, FSL 5.0.9 and AFNI v16.2.07. For more details about the pipeline, see the section corresponding to workflows in fMRIPrep's documentation. MSC和HBN功能性预处理。MSC和HBN数据集中的功能图像使用基于Nipype 1.1.9的fMRIPrep 1.3.2进行预处理。fMRIPrep的预处理描述基于软件中分发的模板，其受“无版权保留”（CC0）许可证保护。fMRIPrep的内部操作使用Nilearn 0.5.0，ANTs 2.2.0，FreeSurfer 6.0.1，FSL 5.0.9和AFNI v16.2.07。有关管道的更多详细信息，请参阅fMRIPrep文档中与工作流程对应的部分。
T1w images were corrected for intensity non-uniformity with N4BiasFieldCorrection , distributed with ANTs and used as T1w-reference throughout the workflow. The T1w-reference was then skull-stripped with a Nipype implementation of the antsBrainExtraction.sh workflow, using NKI as the target template. Brain surfaces were reconstructed using recon-all , and the brain mask estimated previously was refined with a custom variation of the method to reconcile ANTs-derived and FreeSurfer-derived segmentations of the cortical gray matter using Mindboggle . Spatial normalization to the ICBM 152 Nonlinear Asymmetrical template version was performed through nonlinear registration with antsRegistration, using brain-extracted versions of both T1w volume and template. Brain tissue segmentation of cerebrospinal fluid, white matter and gray matter was performed on the brain-extracted T1w images using FSL's fast . T1w图像使用ANTs中的N4BiasFieldCorrection进行强度非均匀性校正，并在整个工作流程中作为T1w参考。然后使用Nipype实现的antsBrainExtraction.sh工作流程对T1w参考进行头骨剥离，使用NKI作为目标模板。使用recon-all重建脑表面，并使用Mindboggle对先前估计的脑部掩模进行优化，以调和ANTs和FreeSurfer推导的皮层灰质分割。通过antsRegistration进行非线性配准，使用T1w体积和模板的脑提取版本，将空间标准化到ICBM 152非线性不对称模板版本。使用FSL的fast在脑提取的T1w图像上执行脑组织分割，包括脑脊液、白质和灰质。
Functional data were slice-time corrected using AFNI's 3dTshift and motion corrected using FSL's mcflirt . Fieldmap-less distortion correction was performed by co-registering the functional image to the same-participant T1w image with intensity inverted and constrained with an average fieldmap template , implemented with antsRegistration. This was followed by co-registration to the corresponding T1w image using boundary-based registration with of freedom. Motion-correcting transformations, field-distortion-correcting warp, BOLD-to-T1w transformation and T1w-to-template (MNI) warp were concatenated and applied in a single step using antsApplyTransforms using Lanczos interpolation. Several confounding time series were calculated based on this pre-processed BOLD: framewise displacement (FD), DVARS and three region-wise global signals. FD and DVARS are calculated for each functional run, both using their implementations in Nipype . The three global signals are extracted within the cerebrospinal fluid, the white matter and the whole-brain masks. The resultant nifti file for each MSC and HBN individual who participated in this study followed the file naming pattern *space-T1w_desc-preproc_bold.nii.gz. 功能数据使用AFNI的3dTshift进行时间切片校正，并使用FSL的mcflirt进行运动校正。无场图畸变校正通过将功能图像与相同参与者的T1w图像配准并进行强度反转来实现，并使用平均场图模板进行约束，采用antsRegistration实现。然后使用基于边界的配准将其配准到相应的T1w图像，自由度为。运动校正变换、场畸变校正变形、BOLD到T1w变换和T1w到模板（MNI）变形被连接并使用Lanczos插值在单个步骤中应用，使用antsApplyTransforms。基于这些预处理的BOLD计算了几个混杂时间序列：帧间位移（FD）、DVARS和三个区域全局信号。FD和DVARS分别针对每个功能运行计算，均使用Nipype中的实现。三个全局信号在脑脊液、白质和整个脑掩模内提取。 参与本研究的每个 MSC 和 HBN 个体的 nifti 文件遵循文件命名模式 *space-T1w_desc-preproc_bold.nii.gz。
Image quality control. All functional images in the HCP and MSC datasets were retained. The quality of functional images in the MSC and HBN datasets were assessed using fMRIPrep's visual reports and MRIQC 0.15 .1 (ref. ). Data were visually inspected for whole-brain field of view coverage, signal artifacts and proper alignment to the corresponding anatomical image. Functional data were excluded if more than of the frames exceeded . Furthermore, HBN functional data were excluded if marked as an outlier (exceeding 1.5x interquartile range (IQR) in the adverse direction) in more than half of the following image quality metrics (calculated within datasets, across all functional acquisitions): dvars, tsnr, fd mean, aor, aqi, snr and efc. Information about these image quality metrics can be found in MRIQC's documentation. 图像质量控制。保留了 HCP 和 MSC 数据集中的所有功能图像。使用 fMRIPrep 的视觉报告和 MRIQC 0.15.1（参考 ）评估了 MSC 和 HBN 数据集中功能图像的质量。数据经过视觉检查，检查了整个大脑的视野覆盖范围、信号伪影以及与相应解剖图像的正确对齐。如果功能数据中超过 的帧超过 ，则排除功能数据。此外，如果 HBN 功能数据在以下图像质量指标中被标记为异常值（在所有功能采集中计算的数据集内，超过 1.5 倍四分位距（IQR）的逆向方向），则排除功能数据：dvars、tsnr、fd mean、aor、aqi、snr 和 efc。有关这些图像质量指标的信息可以在 MRIQC 的文档中找到。
Functional and structural networks pre-processing. Parcellation preprocessing. A functional parcellation designed to optimize both local gradient and global similarity measures of the fMRI signal (Schaefer200) was used to define 200 areas on the cerebral cortex. These nodes are also mapped to the Yeo canonical functional networks . For the HCP dataset, the Schaefer200 is openly available in '32k fs LR' space as a CIFTI file. For the MSC and HBN datasets, a Schaefer200 parcellation was obtained for each participant using a Gaussian classifier surface atlas (trained on 100 unrelated HCP participants) and FreeSurfer's mris_ca_label function. These tools use the surface registrations computed in the recon-all pipeline to transfer a group average atlas to subject space based on individual surface curvature and sulcal patterns. This method rendered a T1w space volume for each participant. For use with functional data, the parcellation was resampled to 2-mm T1w space. This process could be repeated for other resolutions of the parcellation (that is, Schaefer100). 功能和结构网络预处理。分区预处理。设计用于优化fMRI信号的局部梯度和全局相似度测量的功能分区（Schaefer200）被用来定义大脑皮层上的200个区域。这些节点也映射到Yeo标准功能网络。对于HCP数据集，Schaefer200以'CIFTI'文件的形式在'32k fs LR'空间中公开提供。对于MSC和HBN数据集，使用高斯分类器表面图谱（在100个不相关的HCP参与者上进行训练）和FreeSurfer的mris_ca_label功能为每个参与者获得了Schaefer200分区。这些工具使用在recon-all管道中计算的表面配准来基于个体表面曲率和沟回模式将群体平均图谱转移到个体空间。该方法为每个参与者生成了T1w空间体积。用于功能数据时，分区被重采样到2mm T1w空间。这个过程可以针对分区的其他分辨率（即Schaefer100）重复进行。
Functional network pre-processing. Each pre-processed BOLD image was linearly de-trended, band-pass filtered , confound regressed and standardized using Nilearn signal.clean, which removes confounds orthogonally to the temporal filters . The confound regression employed included six motion estimates; time series of the mean cerebrospinal fluid, mean white matter and mean global signal; the derivatives of these nine regressors; and the squares of these 18 terms. Furthermore, a spike regressor was added for each fMRI frame exceeding a motion threshold root mean squared displacement; and FD). This confound strategy has been shown to be a relatively effective option for reducing motion-related artifacts . After pre-processing and nuisance regression, residual mean BOLD time series at each node were recovered. eFC matrices for each participant were computed and then averaged across participants to obtain a representative eFC matrix for each dataset. This processing was performed for both resting-state and movie-watching data. 功能网络预处理。每个预处理的BOLD图像都经过线性去趋势、带通滤波、混杂回归和标准化处理，使用Nilearn signal.clean进行处理，该处理方法可以正交地去除混杂因素和时间滤波器。混杂回归包括六个运动估计；平均脑脊液、平均白质和平均全局信号的时间序列；这九个回归因子的导数；以及这18个项的平方。此外，对于每个超过运动阈值（均方根位移和FD）的fMRI帧，还添加了一个尖峰回归因子。这种混杂策略已被证明是减少与运动相关的伪影的相对有效选项。在预处理和干扰回归之后，每个节点的残余平均BOLD时间序列被恢复。为每个参与者计算eFC矩阵，然后对参与者进行平均，以获得每个数据集的代表性eFC矩阵。这个处理过程对于静息态和观影数据都进行了处理。
Edge graph construction. Constructing networks from fMRI data (or any neural time series data) requires estimating the statistical dependency between every pair of time series. The magnitude of that dependency is usually interpreted as a measure of how strongly (or weakly) those voxels or parcels are functionally connected to each other. By far the most common measure of statistic dependence is the Pearson correlation coefficient. Let and 边缘图构建。从 fMRI 数据（或任何神经时间序列数据）构建网络需要估计每对时间序列之间的统计依赖关系。该依赖关系的大小通常被解释为衡量这些体素或包裹之间功能连接强度（或弱度）的指标。迄今为止，最常见的统计依赖度量是 Pearson 相关系数。让 和
be the time series recorded from voxels or parcels and , respectively. We can calculate the correlation of and by first scoring each time series, such that at where and are the time-averaged mean and s.d. Then, the correlation of and can be calculated as . Repeating this procedure for all pairs of parcels results in a node-by-node correlation matrix-that is, an estimate of functional connectivity. If there are nodes, this matrix has dimensions . 分别是从体素或包裹 和 记录的时间序列。我们可以通过首先 对每个时间序列进行评分来计算 和 的相关性，其中 处 和 是时间平均值和标准差。然后， 和 的相关性可以计算为 。对所有包裹对重复此过程会产生一个节点对节点的相关性矩阵-即功能连接的估计。如果有 个节点，则此矩阵的维度为 。
To estimate edge-centric networks, we need to modify the above approach in one small but crucial way. Suppose we have two -scored parcel time series, and . To estimate their correlation, we calculate the mean of their element-wise product (not exactly the average, because we divide by rather than ). Suppose, instead, that we never calculate the mean and simply stop after calculating the element-wise product. This operation would result in a vector of length whose elements encode the moment-by-moment co-fluctuations magnitude of parcels and . For instance, suppose at time , parcels and simultaneously increased their activity relative to baseline. These increases are encoded in and as positive entries in the th position, so their product is also positive. The same would be true if and decreased their activity simultaneously (because the product of negatives is a positive). On the other hand, if increased while decreased (or vice versa), this would manifest as a negative entry. Similarly, if either or increased or decreased while the activity of the other was close to baseline, the corresponding entry would be close to zero. 为了估计以边缘为中心的网络，我们需要以一种微小但至关重要的方式修改上述方法。假设我们有两个评分的包裹时间序列，b1 和 b2 。为了估计它们的相关性，我们计算它们的逐元素乘积的均值（不是准确的平均值，因为我们除以 b3 而不是 b4 ）。假设，相反地，我们从不计算均值，而是在计算元素乘积后直接停止。这个操作会导致一个长度为 b5 的向量，其元素编码了包裹 b6 和 b7 的瞬时共同波动的幅度。例如，假设在时刻 b8 ，包裹 b9 和 b10 相对于基准同时增加了它们的活动。这些增加被编码为在第 t 位置的正条目，所以它们的乘积也是正的。如果 b13 和 b14 同时减少了它们的活动（因为负数的乘积是正数），情况也是如此。另一方面，如果 b15 增加了而 b16 减少了（或反之亦然），这会表现为一个负的条目。 同样，如果 或 中的任一个增加或减少，而另一个的活动接近基线，相应的条目将接近零。
Accordingly, the vector resulting from the element-wise product of and can be viewed as encoding the magnitude of moment-to-moment co-fluctuations between and . An analogous vector can easily be calculated for every pair of parcels (network nodes), resulting in a set of co-fluctuation (edge) time series. With parcels, this results in pairs, each of length . From these time series, we can estimate the statistical dependency for every pair of edges. We refer to this construct as eFC. Let and be the time series for edges and , respectively. Then, we can calculate as 因此，由 和 的逐元素乘积得到的向量可以被视为编码 和 之间瞬时共同波动的大小。对于每一对区块（网络节点），都可以轻松计算出类似的向量，从而得到一组共同波动（边缘）时间序列。有 个区块，这将产生 对，每个长度为 。从这些时间序列中，我们可以估计每对边的统计依赖性。我们将这个构造称为 eFC。让 和 分别是边 和 的时间序列。然后，我们可以计算 如下：
Here, the denominator is necessary to bind to the interval . 在这里，分母是必要的，以将 绑定到区间 。
Clustering algorithm. In general, eFC matrices are much larger than traditional nFC matrices. Although most clustering algorithms can be applied to hundreds or even thousands of observations, estimating clusters for eFC (which consists of tens of thousands of observations, each paired with at least as many features) presents a computational challenge, especially if the aim is to explore the space of possible partitions. To address this issue and to cluster eFC, we developed a simple two-step clustering procedure that operates on a low-dimensional representation of the eFC matrix. 聚类算法。通常情况下，eFC矩阵比传统的nFC矩阵要大得多。尽管大多数聚类算法可以应用于数百甚至数千个观测值，但为eFC（由数万个观测值组成，每个观测值都至少与同样多的特征配对）估计聚类存在着计算挑战，特别是如果旨在探索可能分区的空间。为了解决这个问题并对eFC进行聚类，我们开发了一个简单的两步聚类程序，该程序在eFC矩阵的低维表示上运行。
First, we performed an eigen decomposition of the eFC matrix, retaining the top 50 eigenvectors. Eigenvector coefficients were rescaled to the interval by dividing each by its largest magnitude element, and then the rescaled coefficients were simply clustered using a standard -means algorithm with Euclidean distance. We varied the number of communities, , from to , repeating the clustering algorithm 250 times at each value. We retained, as a representative partition, the one with the greatest overall similarity to all other partitions. We note that the edge time series can be clustered directly and that, in general, the results were highly similar (Supplementary Fig. 12). 首先，我们对 eFC 矩阵进行特征分解，保留前 50 个特征向量。特征向量系数被重新缩放到区间 ，方法是将每个系数除以其最大幅度元素，然后使用欧氏距离的标准 -means 算法对重新缩放的系数进行简单聚类。我们将社区的数量 从 变化到 ，在每个值上重复聚类算法 250 次。我们保留了作为代表性分区的那个与所有其他分区最相似的分区。我们注意到边缘时间序列可以直接进行聚类，而且一般来说，结果非常相似（附图 12）。
We note that, in general, other community detection algorithms could be used in place of -means. Our decision to use this algorithm was practically motivated, as -means exhibited significantly faster runtimes than other algorithms-for example, modularity maximization and Infomap , which have been used extensively in previous work to derive communities in both functional and structural brain networks. 我们注意到，一般来说，其他社区检测算法可以用来替代 -means。我们决定使用这个算法是出于实际动机，因为 -means 的运行时间明显比其他算法快，例如，模块化最大化 和 Infomap ，这些算法在以前的工作中被广泛用于推导功能和结构脑网络中的社区。
Community overlap metrics. The clustering algorithm partitioned edges into non-overlapping clusters. That is, every edge , where , was assigned to one of the clusters. In this list of edges, each node appeared times (we excluded self-connections). Region 's participation in cluster was calculated as 社区重叠度量。聚类算法将边分成不重叠的簇。也就是说，每条边 ，其中 ，被分配到 个簇中的一个。在这些边的列表中，每个节点出现 次（我们排除了自连接）。区域 参与簇 的计算如下：
where was the cluster assignment of the edge linking nodes and , and is the Kronecker delta, whose value is 1 if and 0 otherwise. By definition, , and we can treat the vector as a probability distribution. The entropy of this distribution measures the extent to which region i's community affiliations are distributed evenly across all communities (high entropy and high overlap) or concentrated within a small number of communities (low entropy and low overlap). We calculate this entropy as: 其中 是连接节点 和 的边的簇分配， 是 Kronecker δ，其值为 1，如果 ，否则为 0。根据定义， ，我们可以将向量 视为概率分布。该分布的熵度量了区域 i 的社区隶属关系均匀分布在所有社区中的程度（高熵和高重叠）或者集中在少数几个社区中（低熵和低重叠）。我们计算这个熵为：
To normalize this measure and bind it to the interval [0,1], we divided by . We refer to this measure as community entropy and interpret this value as an index of overlap. Intuitively, as the distribution of edge community assignments approaches uniformity, its normalized entropy is close to 1; when edges are assigned to a single community, normalized entropy is closer to 0 . 为了将这个度量标准归一化并绑定到区间[0,1]，我们除以 。我们将这个度量标准称为社区熵，并将这个值解释为重叠的指数。直观地说，当边的社区分配分布接近均匀时，其归一化熵接近 1；当边被分配到单个社区时，归一化熵更接近 0。
Edge community similarity. When we cluster an eFC matrix, we assign each edge to a single community. These edge communities can be rearranged into the upper triangle of an matrix, , whose element denotes the edge community assignment of the edge between nodes and . The th column of , which we denote as , encodes the community labels of all edges in which node participates. Note that we do not consider self-edges, so the element is left empty. 边社区相似性。当我们对一个 eFC 矩阵进行聚类时，我们将每条边分配给一个单独的社区。这些边社区可以重新排列成一个 矩阵的上三角形， ，其中元素 表示节点 和 之间的边的社区分配。 的第 列，我们称之为 ，编码了节点 参与的所有边的社区标签。请注意，我们不考虑自环，因此元素 为空。
From this matrix, we can compare the edge communities of nodes and by calculating the similarity of vectors and . Here, we measure that similarity as the fraction of elements in both vectors with the same community label. That is: 从这个矩阵中，我们可以通过计算向量 和 的相似度来比较节点 和 的边界社区。在这里，我们将这种相似度定义为两个向量中具有相同社区标签的元素比例。也就是说：
Here, is the Kronecker delta and takes on a value of 1 when and have the same value but is 0 otherwise. Note the normalization of over because we ignore the self-connections and . Repeating this comparison for all pairs of nodes generates the similarity matrix . 在这里， 是 Kronecker δ，在 和 的值相同时取值为 1，否则为 0。请注意对 的归一化，因为我们忽略了自连接 和 。对所有节点对重复进行此比较会生成相似度矩阵 。
Estimating overlapping community structure from . In this study, we applied a clustering algorithm to eFC, which generates overlapping nodal communities. In contrast, field standard community detection algorithms like Infomap and modularity maximization partition into non-overlapping communities. However, there are non-standard methods that can be applied directly to that generate overlapping communities. These include, but are not limited to, stochastic variational inference for the mixed-membership stochastic block model (SVINET), the Affiliation Graph Model (AGMFIT), Bayesian non-negative matrix factorization (NMF) and thresholded weighted link clustering (ThrLink). 从 估计重叠社区结构。在这项研究中，我们将聚类算法应用于 eFC，生成重叠的节点社区。相比之下，像Infomap 和模块化最大化 这样的领域标准社区检测算法将 划分为非重叠社区。然而，有一些非标准方法可以直接应用于 生成重叠社区。这些方法包括但不限于混合成员随机块模型的随机变分推断（SVINET）、从属图模型（AGMFIT）、贝叶斯非负矩阵分解（NMF）和阈值加权链接聚类（ThrLink）。
We applied these methods to group representative data from the HCP dataset (with the number of communities fixed at ) and compared their patterns of overlap with those obtained from clustering . In general, each of these alternative methods require that the input connectivity matrix contain only positively weighted or binary edges, necessitating that it be thresholded. To do this, we computed the maximum spanning tree of the matrix (to ensure that all nodes form a single connected component) and added edges to this backbone to reach a desired network density. We repeated the following comparisons across densities of and (a range in which negative edges were not retained). For each method, 250 overlapping community structures were recovered. We describe each method in more detail below and summarize the results in Supplementary Fig. 17. 我们将这些方法应用于从HCP数据集中提取代表性 数据（其中社区数量固定为 ），并将它们的重叠模式与从聚类 中获得的模式进行比较。一般来说，这些替代方法中的每一种都要求输入的连接矩阵只包含正权重或二进制边，必须对其进行阈值处理。为此，我们计算了 矩阵的最大生成树（以确保所有节点形成单个连接组件），并向此骨干添加边以达到所需的网络密度。我们在 和 的密度范围内重复了以下比较（在此范围内不保留负边）。对于每种方法，我们恢复了250个重叠的社区结构。我们将在下面更详细地描述每种方法，并在附录图17中总结结果。
The SVINET method employs a mixed-membership stochastic block model algorithm, which is a generative model of network communities based on grouping nodes with similar connectivity patterns . This method has been previously used to demonstrate that the areas of the brain that participate in many cognitive functions also participate in proportionally more communities . This method operates on binary connections; thus, edge weights were discarded. Each run was seeded with a random integer and run for 250 iterations with link sampling. Resulting community assignments with at least membership likelihood were recorded as a membership affiliation. SVINET方法采用了混合成员随机块模型算法，这是一种基于将具有相似连接模式的节点分组的网络社区的生成模型。该方法先前已被用来证明大脑参与许多认知功能的区域也参与了比例更多的社区。该方法基于二进制连接进行操作；因此，边缘权重被丢弃。每次运行都以一个随机整数为种子，并进行250次迭代的链接抽样。至少具有一定成员可能性的结果社区分配被记录为成员隶属关系。
The AGMFIT method employs a generative model of communities based on a bipartite graph structure, linking nodes to communities . The central concept of the AGMFIT algorithm is that communities overlap in a 'tiled' manner, meaning that nodes with overlapping community membership are more densely interconnected than non-overlapping nodes. This model of overlapping structure has been shown to accurately capture core-periphery structure in large-scale social networks. This method operates on binary connections; thus, edge weights were discarded. Each run was seeded with a random integer. AGMFIT方法采用基于二部图结构的社区生成模型，将节点链接到社区。AGMFIT算法的核心概念是社区以“平铺”方式重叠，意味着具有重叠社区成员资格的节点比非重叠节点更密切地相互连接。这种重叠结构模型已被证明能够准确捕捉大规模社交网络中的核心-边缘结构。该方法基于二进制连接运作；因此，边权重被丢弃。每次运行都以随机整数作为种子。
The NMF method employs a probabilistic data reduction model that results in a soft partitioning of the network . This method has been shown to avoid over-fitting communities in synthetic random graph data where no real communities exist. Edge weights were retained for this method, and diagonal entries of the adjacency matrix were set to the nodal degree (as suggested in the documentation). Each run was randomly initialized. Runs that did not produce the desired number of communities were rejected, and sampling continued until 250 partitions were obtained. Resulting community assignments with at least membership likelihood were recorded as membership affiliation. NMF 方法采用概率数据降维模型，导致网络的软分区。已经证明该方法可以避免在合成随机图数据中过度拟合社区，其中不存在真实社区。对于该方法，保留了边权重，并将邻接矩阵的对角线条目设置为节点度数（如文档中建议的）。每次运行都是随机初始化的。未能产生所需数量的社区的运行将被拒绝，并且采样将持续进行，直到获得 250 个分区。至少具有成员资格可能性的结果社区分配被记录为成员资格隶属。
For the ThrLink method, we created a weighted line graph from the thresholded adjacency matrix . This matrix was clustered using the generalized Louvain algorithm with the resolution parameter tuned to produce the desired number of communities. To tune this parameter, a range of values was used to recover communities of varying sizes. The minimum and maximum values producing the desired number of communities were recorded. Uniformly 对于 ThrLink 方法，我们从阈值邻接矩阵创建了加权线图。使用广义 Louvain 算法对该矩阵进行聚类，分辨率参数调整为产生所需数量的社区。为了调整此参数，使用一系列值来恢复不同大小的社区。记录产生所需数量的社区的最小和最大值。统一地
randomly sampled values within this range were used to recover communities of the weighted line graph. Runs that did not produce the desired number of communities were rejected, and sampling continued until 250 partitions were obtained. Community memberships of the weighted line graph were projected to the nodes to gather the overlapping structure. 在此范围内随机抽样的 数值用于恢复加权线图的社区。未能产生所需数量的社区的运行将被拒绝，并继续抽样直到获得 250 个分区。加权线图的社区成员关系被投影到节点上，以获取重叠的结构。
We compared community entropy against a series of related statistics tha can be easily derived from as opposed to eFC. These include static measures of participation coefficient and versatility and the 'dynamic' measure of flexibility . We calculated static measures using a group representative matrix that was the average nFC data from all scans and individuals. Flexibility was calculated first at the single-individual level where time series were divided into ten non-overlapping windows containing samples each (approximately ) and subsequently averaged across individuals. Details of how each measure was calculated are presented below. 我们将社区熵与一系列可轻松从 中派生的相关统计数据进行了比较，相对于 eFC。这些包括参与系数 和多功能性 的静态测量，以及灵活性 的“动态”测量。我们使用了一个代表性群体 矩阵来计算静态测量，这个矩阵是所有扫描和个体的平均 nFC 数据。灵活性首先是在单个个体水平上计算的，时间序列被分成包含 个样本的十个不重叠的窗口（约为 ），然后在个体之间进行平均。下面介绍了每个测量是如何计算的的详细信息。
Participation coefficient measures the uniformity with which a node's connections are distributed across (non-overlapping) communities. Values closer to 1 indicate that connections are distributed evenly. Participation coefficient is calculated as: 参与系数衡量节点连接在（非重叠的）社区中分布均匀的程度。接近1的数值表示连接分布均匀。参与系数的计算公式为：
Here, is the total strength of node , and is the strength of node to community . We calculated several variants of participation coefficient in which we varied how communities were defined. First, we treated the system labels from ref. as a community structure and calculated the participation coefficient with respect to these labels. We also tested a more data-driven procedure in which we used multi-scale modularity maximization to detect the communities of the nFC matrix. In doing so, we used a uniform null model , which is appropriate for correlation matrices and has been used extensively in the neuroimaging community (see ref. as just one example) and systematically varied the resolution parameter over the interval (repeating a Louvain-like algorithm 1,000 times). In all cases, we separately calculated the participation coefficient using for positive and negative connection weights. 这里， 是节点 的总强度， 是节点 对社区 的强度。我们计算了几种参与系数的变体，其中我们改变了社区的定义方式。首先，我们将来自参考文献 的系统标签视为一个社区结构，并针对这些标签计算了参与系数。我们还测试了一种更加数据驱动的方法，即使用多尺度模块化最大化 来检测 nFC 矩阵的社区。在这个过程中，我们使用了一个统一的空模型 ，这对于相关矩阵是合适的，并且在神经影像学社区中被广泛使用（参见参考文献 作为一个例子），并系统地改变了分辨率参数 在区间 内（重复进行类似Louvain算法1000次）。在所有情况下，我们分别计算了使用正连接权和负连接权的参与系数。
We also used the detected communities to estimate regional versatility , which measures the variability of a node's community assignment across repeated runs of a community detection algorithm. We calculated versatility as: 我们还使用检测到的社区来估计区域的多功能性，它衡量了节点在社区检测算法的重复运行中社区分配的变化。我们计算多功能性如下：
For a given value of denotes the fraction of times that nodes and were co-assigned to the same community. We calculated versatility with respect to communities detected using the same values of . 对于给定值的 ，表示节点 和 被分配到同一个社区的比例。我们根据使用相同值的 检测到的社区计算多功能性。
Lastly, we calculated network flexibility, which measures how frequently a brain region changes communities across time. We modeled functional connectivity estimated within each non-overlapping window as a layer in a multi-layer network and a used multi-layer modularity maximization algorith to cluster all layers simultaneously. The result is a node-by-layer matrix of communities whose element indicates the community assignment of node in layer . From this matrix, we calculate flexibility as: 最后，我们计算网络的灵活性，它衡量了大脑区域随时间变化社区的频率。我们将每个非重叠窗口内估计的功能连接建模为多层网络中的一层，并使用多层模块化最大化算法 同时对所有层进行聚类。结果是一个节点-层矩阵，其中元素 表示层 中节点 的社区分配。从这个矩阵中，我们计算灵活性如下：
Here, is the number of layers, and is the Kronecker delta function and is equal to 1 when and is 0 otherwise. In essence, flexibility measures the fraction of times that a node's community assignment changes in successive layers (time points). In addition to the resolution parameter, the output of the multi-layer modularity maximization algorithm depends on a second parameter, , that controls the consistency of communities across layers. We systematically varied these parameters over the ranges and and calculated flexibility for all possible pairs. 这里， 是层数， 是 Kronecker δ 函数，当 时等于 1，否则等于 0。实质上，灵活性度量了节点的社区分配在连续层（时间点）中改变的次数的比例。除了 分辨率参数外，多层模块化最大化算法的输出还取决于第二个参数， ，它控制了层间社区的一致性。我们系统地变化了这些参数在范围 和 并计算了所有可能的 对的灵活性。
Graph theoretic analysis of eFC. We applied graph theoretic measures to the eFC matrix to characterize its topological features . We focused on local measures that characterize features at the level of a network's nodes (in the case of eFC, nodes represent pairs of brain regions). To visualize these measures, we reshaped their values into the upper triangle of a region-by-region matrix (Supplementary Fig. 20). We focused on several different measures: eFC 的图论分析。我们对 eFC 矩阵应用了图论度量，以表征其拓扑特征 。我们关注了能够表征网络节点层面特征的局部度量（在 eFC 的情况下，节点代表大脑区域对）。为了可视化这些度量，我们将它们的值重塑成一个区域-区域矩阵的上三角形式（附图 20）。我们关注了几种不同的度量：
Degree measures separately the total number of positive and negative connections incident upon a given node in the eFC network. 度 分别测量了 eFC 网络中给定节点上正负连接的总数。
Strength is the weighted analog of degree and measures separately the total weight of positive and negative connections incident upon a given node in the eFC network. Both degree and strength tell us, on average, how strongly or weakly a given node in the eFC network interacts with other nodes in the eFC network. 强度 是度的加权模拟，分别测量了 eFC 网络中给定节点上正负连接的总权重。度和强度告诉我们，平均而言，eFC 网络中给定节点与其他节点的相互作用强度或弱度。
Participation coefficient measures the extent to which a node's connections in the eFC network are concentrated within or distributed across edge communities. Values close to 0 mean that a given node in the eFC network interacts primarily with other nodes in its own edge community; values close to 1 mean that a given node in the eFC network interacts uniformly with all edge communities. 参与系数 测量了节点在 eFC 网络中的连接是集中在边缘社区内还是分布在各个边缘社区之间的程度。接近 0 的值意味着 eFC 网络中给定节点主要与其所在的边缘社区中的其他节点相互作用；接近 1 的值意味着 eFC 网络中给定节点与所有边缘社区均匀相互作用。
Betweenness centrality measures the number of shortest paths between pairs of nodes in the eFC network that pass through a given node. In general, betweenness centrality implies that a particular node in the eFC network might occupy a position of importance in the network. 中介中心性衡量了 eFC 网络中通过给定节点的节点对之间的最短路径数量。一般来说，中介中心性意味着 eFC 网络中的特定节点可能在网络中占据重要位置。
Clustering coefficient measures the extent to which a node's neighbors in the eFC network are also connected to one another. 聚类系数衡量了 eFC 网络中一个节点的邻居节点之间相互连接的程度。
Exploratory analyses of brain-behavior relationships using eFC. Correlations of eFC weights with behavior. We also used eFC data to explore brain-behavior relationships . The overall pipeline begins by calculating each participant's edge-by-edge eFC matrix (Supplementary Fig. 21a) and representing its upper triangle elements as a vector (Supplementary Fig. 21b). This procedure is repeated for all individuals in the HCP 100 Unrelated Subjects cohort so that the vectorized is stored in a single matrix (Supplementary Fig. 21c). In parallel, we scored participants' behavioral data and performed principal components analysis, resulting in a set of scores that characterize orthogonal modes of behavioral variability (Supplementary Fig. 21d and Supplementary Table 1). We computed the correlation of scores with rows from the matrix of vectorized eFC matrices (each row represents the eFC for a particular edge-edge interaction (Supplementary Fig. 21e)). Repeating this procedure for all rows results in a vector of correlation coefficients that can be reshaped to fit into the upper triangle of an edge-by-edge matrix, resulting in a correlation map (Supplementary Fig. 21f). This entire process is repeated separately for principal components 1-10 and for scans REST1 and REST2. 使用 eFC 进行大脑行为关系的探索性分析。将 eFC 权重与行为进行相关性分析。我们还使用了 eFC 数据来探索大脑行为关系。整个流程首先计算每个参与者的一对一 eFC 矩阵（附录图 21a），并将其上三角元素表示为一个向量（附录图 21b）。这个过程对 HCP 100 个不相关受试者队列中的所有个体都重复进行，将向量化的矩阵存储在一个单独的矩阵中（附录图 21c）。同时，我们对参与者的行为数据进行评分，并进行主成分分析，得到一组表征行为变化的正交模式的分数（附录图 21d 和附录表 1）。我们计算了分数与向量化的 eFC 矩阵的行的相关性（每一行表示特定边缘-边缘相互作用的 eFC）（附录图 21e）。 重复这个过程对所有行，将得到一组相关系数的向量，可以重新调整以适应一个边对边矩阵的上三角形，从而得到一个相关性地图（附图 21f）。这整个过程分别为主要成分 1-10 和扫描 REST1 和 REST2 重复。
We compared the correlation maps from REST1 and REST2 and found good correspondence (Supplementary Fig. 21h,i). To better interpret these maps, we adopted a community-level analysis (see Supplementary Fig. 22 for a short schematic). Briefly, this involves aggregating and averaging correlation coefficients by edge communities (Supplementary Fig. 22b); comparing the average correlation coefficients against a null distribution obtained using a constrained permutation test (Supplementary Fig. 22c); and performing statistical evaluation, controlling for false discovery rate at the level of communities (Supplementary Fig. 22d). Further details of the permutation test can be found in Supplementary Fig. 18. 我们比较了来自 REST1 和 REST2 的相关性地图，并发现了良好的对应关系（附图 21h，i）。为了更好地解释这些地图，我们采用了一个社区级别的分析（请参阅附图 22 以获取简短的示意图）。简而言之，这涉及通过边缘社区聚合和平均相关系数（附图 22b）；将平均相关系数与使用受限制的置换测试获得的空值分布进行比较（附图 22c）；并进行统计评估，控制社区水平的虚发现率（附图 22d）。有关置换测试的更多细节，请参阅附图 18。
Using this community-level approach, we investigated the relationship between and in greater detail. We note that explains approximately variance in behavioral data (almost three times as much as PC2) and defines a task accuracy/reaction time axis of behavior (Supplementary Fig. 21j,k). We include brief descriptions of the other PCs in Supplementary Table 1. We show the correlation map for with eFC in Supplementary Fig. 211. To illustrate how the community-level analysis facilitates a clearer interpretation of brainbehavior correlations, consider eFC of edges in communities 7 and 9 (the block highlighted in Supplementary Fig. 211). Community 7 links higher-order cognitive areas in the control and default mode networks with visual cortex, forming an 'executive-visual' complex, whereas community 9 links control and default mode to the salience/ventral attention network as part of an 'executive-insular' complex (Supplementary Fig. ). Accordingly, the positive correlation eFC between community 7 and 9 with PC1 means that, as the edges within those communities become more synchronized across time (stronger ), the value of increases proportionally (Supplementary Fig. 21o,p). 利用这种社区级的方法，我们更详细地调查了 和 之间的关系。我们注意到 大约解释了行为数据中的 方差（几乎是PC2的三倍），并定义了一个行为的任务准确性/反应时间轴（附图21j，k）。我们在附表1中包含其他主成分的简要描述。我们展示了 与eFC的相关性图（附图211）。为了说明社区级分析如何促进对脑行为相关性的更清晰解释，请考虑社区7和9中边缘的eFC（在附图211中突出显示的区块）。社区7将控制和默认模式网络中的高阶认知区域与视觉皮层连接起来，形成一个“执行-视觉”复合体，而社区9将控制和默认模式连接到显著性/腹侧注意网络，作为一个“执行-岛叶”复合体的一部分（附图 ）。 因此，社区 7 和 9 之间的正相关 eFC 与 PC1 之间的关系意味着，随着这些社区内的边在时间上变得更加同步（更强 ）， 的值会成比例增加（附图 21o，p）。
In addition to modeling brain-behavior relationships using the original eFC data, we repeated this same analysis with residual eFC after regressing out the effect of nFC. Specifically, we used the procedure described in Fig. 2c to generate an approximation of eFC using only data. We then regressed out the approximated from the actual and assessed brain-behavior relationships using the residual values. As with the previous analysis, we found that brainbehavior correlation maps were reproducible across scan sessions (Supplementary Fig. 23). 除了使用原始 eFC 数据建模大脑行为关系外，我们还通过在回归 nFC 效应后重复相同的分析来进行了分析。具体来说，我们使用图 2c 中描述的程序仅使用 数据生成 eFC 的近似值。然后，我们从实际 中回归出近似值 ，并使用残差值评估大脑行为关系。与先前的分析一样，我们发现大脑行为相关性图在扫描会话中是可重复的（附图 23）。
Correlations of regional statistics with behavior. We also compared and brain-behavior relationships by deriving a series of regional (local) network statistics from each and calculating the correlations of behavioral measures with these statistics (Supplementary Fig. 24). We note that the measures derived from both and have identical dimensionality, effectively accounting for any differences in the dimensionality of the original and matrices. In general, we found that the correlation patterns estimated using nFC-derived statistics were highly similar to one another, whereas the correlation pattern derived from the eFC statistic was dissimilar (Supplementary Fig. 24f). 区域统计与行为的相关性。我们还通过从每个派生一系列区域（局部）网络统计量并计算行为测量与这些统计量的相关性（补充图 24）来比较 和 脑行为关系。我们注意到，从 和 派生的测量具有相同的维度，有效地解释了原始 和 矩阵维度的任何差异。总的来说，我们发现使用 nFC 派生统计量估计的相关性模式彼此非常相似，而使用 eFC 统计量派生的相关性模式不同（补充图 24f）。
These findings demonstrate that has the potential to uniquely explain patterns of inter-individual variability not currently explainable by , opening new opportunities for studying individual differences in individuals' cognitive, developmental and clinical states. 这些发现表明， 有潜力独特地解释目前无法解释的个体间变异模式，为研究个体认知、发展和临床状态的差异提供了新机会。
Modeling eFC in terms of nFC. and are both derived from the same substrate: regional fMRI BOLD time series. Can the eFC between edges and be easily modeled in terms of nFC? We tested whether this was the case using 以 nFC 为基础对 eFC 进行建模。 和 都源自相同的底物：区域 fMRI BOLD 时间序列。边缘 和 之间的 eFC 能否轻松地以 nFC 为基础进行建模？我们使用线性回归来测试是否如此。
linear regression to explain the eFC between pairs of edges and using information about the pairwise among the same set of nodes: , and . We considered two classes of models. The first modeled eFC in terms of the six weights: 用信息解释边缘对 和 之间的 eFC，信息来自于相同节点集合中的成对 ： ， 和 。我们考虑了两类模型。第一类模型以六个 权重来建模 eFC：
The second modeled in terms of interactions: 第二类模型以 交互来建模 ：
In this model, we systematically varied the interaction term, , so that we tested all possible pairs of edges. 在这个模型中，我们系统地变化了交互项， ，以便测试所有可能的边对。
In general, we found that neither model 1 nor model 2 could fully reproduce eFC. Model 1 performed particularly poorly . The results of model 2 were more varied. When all nodes were represented in the interaction term-for example, -the model performed well , consistent with what we reported in Fig. 2c. When any node is repeated-for example, -the model performed poorly 总的来说，我们发现模型 1 和模型 2 都无法完全复制 eFC。模型 1 表现特别糟糕 。模型 2 的结果更加多样化。当所有节点都在交互项中表示时，例如， ，模型表现良好 ，与我们在图 2c 中报告的一致。当任何节点重复时，例如， ，模型表现不佳 。
Collectively, these observations suggest that eFC is not well approximated using linear combinations of , but, with nonlinear transformations and inclusion of interaction terms, can approximate eFC. However, these transformations are unintuitive, and the approximation still fails to fully explain variance in . 总的来说，这些观察结果表明，使用线性组合的 不能很好地近似 eFC，但是，通过非线性转换和包含交互项， 可以近似 eFC。然而，这些转换是不直观的，而且这种近似仍然无法完全解释 中的方差。
Statistics. All statistical comparisons made between individuals and groups were implemented using paired sample and two-sample -tests, ANOVAs or permutation tests. For -tests and ANOVAs, the data distribution was assumed to be normal, but this was not formally tested. We used several variants of permutation tests: in Fig. 7b,e,f, we permuted condition labels (REST and MOVIE); in Fig. 7g, we permuted system labels; in Supplementary Figs. 21 and 22 , we mapped edge communities into a region-by-region matrix and permuted its rows and columns before extracting the permuted edge community labels (Supplementary Figs. 18 and 24). For permutation tests, observed values were scored with respect to the mean and s.d. estimated for the null distribution and converted into values. 统计。所有个体和群体之间的统计比较均使用成对样本和双样本 -检验、方差分析或置换检验进行。对于 -检验和方差分析，数据分布被假定为正态分布，但并未进行正式检验。我们使用了几种置换检验的变体：在图 7b、e、f 中，我们对条件标签（REST 和 MOVIE）进行了置换；在图 7g 中，我们对系统标签进行了置换；在补充图 21 和 22 中，我们将边缘社区映射到区域-区域矩阵中，并在提取置换的边缘社区标签之前对其行和列进行了置换（补充图 18 和 24）。对于置换检验，观察值被 得分，以便与空分布的均值和标准差进行比较，并转换为 值。
Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article. 报告摘要。有关研究设计的更多信息，请参阅与本文相关的《自然研究报告摘要》。
Data availability 数据可用性
All imaging data come from publicly available, open access repositories. Human Connectome Project data can be accessed at https://db.humanconnectome.org/ app/template/Login.vm after signing a data use agreement. Midnight Scan Club data can be accessed via OpenNeuro at https://openneuro.org/datasets/ds000224/ versions/1.0.1. The Healthy Brain Network Serial Scanning Initiative data can be accessed at https://fcon_1000.projects.nitrc.org/indi/hbn_ssi/download.html. 所有成像数据均来自公开可用的开放存储库。人类连接组计划数据可在 https://db.humanconnectome.org/ app/template/Login.vm 签署数据使用协议后访问。午夜扫描俱乐部数据可通过 OpenNeuro 在 https://openneuro.org/datasets/ds000224/ versions/1.0.1 访问。健康大脑网络串行扫描计划数据可在 https://fcon_1000.projects.nitrc.org/indi/hbn_ssi/download.html 访问。
Code availbility 代码可用性
Code to compute eFC and its related derivatives has been made available at https:// github.com/brain-networks. 计算 eFC 及其相关衍生物的代码已在 https://github.com/brain-networks 上提供。
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Acknowledgements 致谢
This research was supported by the Indiana University Office of the Vice President for Research Emerging Area of Research Initiative, Learning: Brains, Machines and Children (F.Z.E. and R.F.B.). This material is based on work supported by the National Science Foundation Graduate Research Fellowship under grant no. 1342962 (J.F.). This research was supported, in part, by the Lilly Endowment, through its support for the Indiana University Pervasive Technology Institute and, in part, by the Indiana METACyt Initiative. The Indiana METACyt Initiative at Indiana University was also supported, in part, by the Lilly Endowment. Data were provided, in part, by the Human Connectome Project, WU-Minn Consortium (principal investigators: D. Van Essen and K. Ugurbil; 1U54MH091657), funded by the 16 National Institues of Health (NIH) institutes and centers that support the NIH Blueprint for Neuroscience Research and by the McDonnell 这项研究得到了印第安纳大学研究副校长办公室新兴研究领域计划的支持，学习：大脑、机器和儿童（F.Z.E.和 R.F.B.）。该材料基于得到国家科学基金会研究生研究奖学金支持的工作，资助号为 1342962（J.F.）。这项研究部分得到了 Lilly 捐赠的支持，通过其支持印第安纳大学普适技术研究所，以及印第安纳 METACyt 计划的支持。印第安纳大学的 METACyt 计划也得到了 Lilly 捐赠的部分支持。数据部分由人类连接组项目提供，WU-Minn 联合体（首席研究员：D. Van Essen 和 K. Ugurbil；1U54MH091657）资助，该项目由支持神经科学研究的 16 个国家卫生研究院（NIH）研究所和中心以及 McDonnell
Center for Systems Neuroscience at Washington University. We thank B. Mišić for reading an early version of this manuscript. 华盛顿大学系统神经科学中心。我们感谢 B. Mišić阅读本手稿早期版本。
Author contributions 作者贡献
J.F. and R.F.B. conceived of the study, processed data, carried out all analyses and wrote the first draft of the manuscript. F.Z.E., Y.J. and O.S. contributed to project direction via discussion. All authors helped revise and write the submitted manuscript. J.F.和 R.F.B.构思了这项研究，处理数据，进行了所有分析并撰写了手稿的初稿。F.Z.E.，Y.J.和 O.S.通过讨论为项目方向做出了贡献。所有作者都帮助修订和撰写了提交的手稿。
Competing interests 竞争利益
The authors declare no competing interests. 作者声明没有竞争利益。
Additional information 附加信息
Supplementary information is available for this paper at https://doi.org/10.1038/ s41593-020-00719-y. 有关本文的补充信息，请访问 https://doi.org/10.1038/s41593-020-00719-y。
Correspondence and requests for materials should be addressed to R.F.B. 信函和材料请求应寄至 R.F.B.
Peer review information Nature Neuroscience thanks Lucina Uddin, Andrew Zalesky, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. 自然神经科学感谢 Lucina Uddin、Andrew Zalesky 和其他匿名审稿人对本工作的同行评审所做的贡献。
Reprints and permissions information is available at www.nature.com/reprints. 重印和权限信息可在 www.nature.com/reprints 获取。
natureresearch 自然研究
Nature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Research policies, see Authors & Referees and the Editorial Policy Checklist. 自然研究希望提高我们发表的工作的可重复性。此表提供了一致性和透明度的结构以供报告。有关自然研究政策的更多信息，请参阅作者和审稿人以及编辑政策清单。
Statistics 统计
For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section. 对于所有统计分析，请确认以下项目是否出现在图例、表图例、主文本或方法部分中。
n/a Confirmed 无法确认
The exact sample size for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly The statistical test(s) used AND whether they are one- or two-sided 每个实验组/条件的确切样本量 ，以离散数字和测量单位给出，说明是否从不同样本中进行测量还是重复测量同一样本使用的统计检验以及它们是单侧还是双侧的声明
Only common tests should be described solely by name; describe more complex techniques in the Methods section. 只有常见测试应仅通过名称描述；将更复杂的技术描述在方法部分。
A description of all covariates tested 所有被测试协变量的描述
A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons 所有假设或校正的描述，例如正态性检验和多重比较的调整
A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) 统计参数的完整描述，包括中心趋势（例如均值）或其他基本估计（例如回归系数）和变异性（例如标准差）或相关的不确定性估计（例如置信区间）
For null hypothesis testing, the test statistic (e.g. F, ) with confidence intervals, effect sizes, degrees of freedom and value noted Give values as exact values whenever suitable. 对于零假设检验，使用检验统计量（例如 F， ）与置信区间、效应量、自由度和 值进行注释。在合适的情况下，将 值给出为精确值。
For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings 对于贝叶斯分析，提供有关先验选择和马尔可夫链蒙特卡洛设置的信息
For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes 对于层次和复杂设计，确定适当的测试水平并全面报告结果
Estimates of effect sizes (e.g. Cohen's , Pearson's ), indicating how they were calculated 效应大小的估计（例如，科恩的 ，皮尔逊的 ），指示计算方法
Our web collection on statistics for biologists contains articles on many of the points above. 我们为生物学家收集的统计信息网络包含许多上述内容的文章。
Software and code 软件和代码
Policy information about availability of computer code 计算机代码可用性政策信息
Data collection 数据收集
All data used in this study is publicly available. The authors of this study did not write custom code to collect any of this data; therefore the authors did not use software for data collection. 本研究中使用的所有数据均为公开可用。本研究的作者未编写自定义代码来收集任何数据；因此，作者未使用软件进行数据收集。
Data analysis 数据分析
Human Connectome Project data are provided already minimally preprocessed at the ConnectomeDB (https:/db.humanconnectome.org/ app/template/Login.vm). Midnight Scan Club and Healthy Brain Network fMRI data were preprocessed with fMRIPrep version 1.3.2. fMRIPrep can be found here: https://github.com/poldracklab/fmriprep. fMRIPrep uses Nipype 1.1.9, Nilearn 0.5.0, ANTs 2.2.0, FreeSurfer 6.0.1, FSL 5.0.9, AFNI v16.2.07, and Mindboggle [RRID:SCR_002438]. Subject specific parcellations were fit with FreeSurfer 6.0.1 using code available here: https://github.com/faskowit/multiAtlasTT and data available here: https://figshare.com/articles/ multiAtlasTT_data_hcptrained/7552853. fMRI data were nuisance regressed with code available here: https://github.com/faskowit/appfmri-2-mat which uses Nilearn's signal.clean, from Nilearn 0.5.0. Custom MATLAB (version 2019a) code was used for analyzing eFC. Upon manuscript acceptance, functions to generate and analyze edge time series and eFC will be released as a repository on the Brain Networks & Behavior Lab Github: https://github.com/brain-networks/. Custom MATLAB to fit alternative overlapping algorithms is available here: https://github.com/faskowit/overlap_on_NxN_func. 人类连接组计划数据已经在ConnectomeDB（https:/db.humanconnectome.org/ app/template/Login.vm）上进行了最小预处理。午夜扫描俱乐部和健康大脑网络的fMRI数据已经使用fMRIPrep版本1.3.2进行了预处理。fMRIPrep可以在这里找到：https://github.com/poldracklab/fmriprep。fMRIPrep使用Nipype 1.1.9、Nilearn 0.5.0、ANTs 2.2.0、FreeSurfer 6.0.1、FSL 5.0.9、AFNI v16.2.07和Mindboggle [RRID:SCR_002438]。使用FreeSurfer 6.0.1拟合了特定主题的分区，代码可在此处找到：https://github.com/faskowit/multiAtlasTT，数据可在此处找到：https://figshare.com/articles/multiAtlasTT_data_hcptrained/7552853。fMRI数据使用了可在此处找到的代码进行干扰回归：https://github.com/faskowit/appfmri-2-mat，该代码使用了Nilearn 0.5.0中的signal.clean。用于分析eFC的自定义MATLAB（版本2019a）代码已经被使用。在手稿被接受后，用于生成和分析边缘时间序列和eFC的函数将作为Brain Networks & Behavior Lab Github上的存储库发布：https://github.com/brain-networks/。用于拟合替代重叠算法的自定义MATLAB代码可以在此处找到：https://github.com/faskowit/overlap_on_NxN_func.
For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors/reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Research guidelines for submitting code & software for further information. 对于使用自定义算法或软件的手稿，这些算法或软件对研究至关重要，但尚未在已发表的文献中描述，软件必须提供给编辑/审稿人。我们强烈建议将代码存储在社区代码库中（例如 GitHub）。有关提交代码和软件的更多信息，请参阅《自然研究指南》。
Data 数据
Policy information about availability of data 数据可用性政策信息
All manuscripts must include a data availability statement. This statement should provide the following information, where applicable: 所有手稿必须包含数据可用性声明。该声明应提供以下信息（如适用）：
Accession codes, unique identifiers, or web links for publicly available datasets 公开可用数据集的存取代码、唯一标识符或网页链接
A list of figures that have associated raw data 具有关联原始数据的数字列表
A description of any restrictions on data availability 有关数据可用性的任何限制描述
All imaging data come from publicly-available, open-access repositories. Human Connectome Project data can be accessed via (https://db.humanconnectome.org/ 所有成像数据均来自公开可用的开放存储库。人类连接组计划数据可通过（https://db.humanconnectome.org/）访问。
Field-specific reporting 领域特定报告
Please select the one below that is the best fit for your research. If you are not sure, read the appropriate sections before making your selection. 请选择以下最适合您研究的选项。如果不确定，请在选择之前阅读相应部分。
All studies must disclose on these points even when the disclosure is negative. 所有研究必须在这些要点上披露，即使披露是负面的。
Sample size Three human neuroimaging datasets were used in this study: Human Connectome Project (HCP), Midnight Scan Club (MSC), and Health Brain Network Serial Scanning Initiative (HBN). For HCP, we used a publicly available list of 100 unrelated subjects. For MSC, the dataset consists of 10 subjects. For HBN, the dataset consists of 13 subject; due to limited availability of low motion fMRI scans, 3 subjects of HBN were excluded. Each of the three datasets were chosen to provide data to demonstrate aspects of the novel eFC construct. The 100 unrelated HCP subjects were utilized for constructing EFC from a large unrelated (the data is a subset of a large twins study) cohort of high-quality neuroimaging data. The MSC data was utilized for demonstrating reliability of eFC, given that MSC subjects have 10 resting state scans each. The HBN dataset was utilized from demonstrating how passive movie watching could affect eFC, since for this dataset multiple resting and movie-watching scans were acquired. No statistical methods were used to pre-determine sample sizes, but our sample sizes are similar to those reported in previous publications and represent either all usable data (MSC, HBN) or a subset preselected by the study coordinators (HCP) 样本量本研究使用了三个人类神经影像数据集：人类连接组计划（HCP）、午夜扫描俱乐部（MSC）和健康大脑网络连续扫描倡议（HBN）。对于 HCP，我们使用了一个公开的包含 100 个不相关受试者的名单。对于 MSC，数据集包括 10 个受试者。对于 HBN，数据集包括 13 个受试者；由于低运动 fMRI 扫描的可用性有限，HBN 的 3 个受试者被排除在外。选择了这三个数据集以提供数据来展示新型 eFC 构建的各个方面。利用了 100 个不相关的 HCP 受试者来构建来自高质量神经影像数据的大型不相关（数据是大型双生子研究的子集）队列的 EFC。MSC 数据用于展示 eFC 的可靠性，因为 MSC 受试者每人有 10 个静息态扫描。HBN 数据集用于展示被动观影如何影响 eFC，因为对于这个数据集，获取了多个静息和观影扫描。没有使用统计方法来预先确定样本量，但我们的样本量与先前出版物中报告的相似，并且代表了所有可用数据（MSC，HBN）或由研究协调员预先选择的子集（HCP）
Data exclusions Three subjects of the HBN dataset were excluded from our study for having little to no MRI data that passed our data exclusion criteria. Individual HBN fMRI were excluded based on image quality metrics (IQMs) output from MRIQC. The MRIQC package was designed to automatically provide IQMs and individual and group visual reports using reproducible containerization technology. The following IQMs were used: dvars, tsnr, fd mean, aor, aqi,, snr, and efc. Individual scans were excluded if the IQMs for the scan exceeded 1.5 times the inter-quartile range of the distribution (in the adverse direction) of a particular IQM across the dataset, for five or more of the IQMs. Individual scans were also excluded if more than of frames exceeded frame-wise displacement. Code to implement this filtering can be found at: https://github.com/faskowit/filter_mriqc_res. The IQM exclusion criteria have not been employed in this manner in a previous study. The framewise displacement exclusion criteria were partly based on Parkes et al. (2018) Neurolmage. These exclusion criteria were preestablished for HBN. All scans from HCP and MSC were retained; this was also pre-established. All data were visually inspected for artifacts. Furthermore, in Supplementary Figure 2 we demonstrate that after censoring high motion frames in the HCP data, the correlation of edge amplitude with motion does not substantially change. 数据排除 根据我们的数据排除标准，HBN数据集中的三个受试者被排除在我们的研究之外，因为他们的MRI数据很少或没有通过我们的数据排除标准。个体HBN fMRI根据从MRIQC输出的图像质量度量（IQMs）进行排除。MRIQC软件包旨在利用可重现的容器化技术自动提供IQMs和个体以及群体的可视报告。使用了以下IQMs：dvars、tsnr、fd mean、aor、aqi、snr和efc。如果某个扫描的IQMs超过了数据集中特定IQM的四分位距的1.5倍（向不利方向）五个或更多的IQMs，那么将排除个体扫描。如果超过 帧的 帧位移超过了，则也将排除个体扫描。实施此过滤的代码可在以下链接找到：https://github.com/faskowit/filter_mriqc_res。以这种方式使用IQM排除标准在先前的研究中尚未被采用。帧位移排除标准部分基于Parkes等人（2018）的《神经影像学》。这些排除标准已经为HBN预先设定。 所有来自 HCP 和 MSC 的扫描都被保留；这也是事先设定的。所有数据都经过目视检查以检测伪影。此外，在补充图 2 中，我们展示了在 HCP 数据中审查高运动帧后，边缘幅度与运动的相关性并没有发生实质性变化。
Replication Supplemental Figure 3 shows the correlation of eFC data across three independent datasets (HCP, MSC, and HBN). Supplemental Figure 4 shows the correlation of eFC data from HCP, processed with difference nuisance regression strategies. Supplemental Figure 11 shows the normalized entropy maps for each dataset (HCP, MSC, HBN). Supplemental Figure 13 shows the normalized entropy maps across number of communities ( ) in the HCP dataset. Supplemental Figure 14 shows the normalized entropy maps across three alternative parcellations (Desikan-Killiany, Destrieux, and Brainnetome) of the cortex. The authors consider all of these to be instances of successful replication regarding concepts related to the novel eFC construct. 复制补充图 3 显示了三个独立数据集（HCP、MSC 和 HBN）之间 eFC 数据的相关性。补充图 4 显示了使用不同干扰回归策略处理的 HCP 数据的 eFC 数据的相关性。补充图 11 显示了每个数据集（HCP、MSC、HBN）的归一化熵图。补充图 13 显示了 HCP 数据集中社区数量（ ）的归一化熵图。补充图 14 显示了皮层的三种替代分区（Desikan-Killiany、Destrieux 和 Brainnetome）的归一化熵图。作者认为所有这些都是关于新 eFC 结构相关概念的成功复制实例。
Randomization Subjects were not partitioned into groups. Data from each cohort (HCP, MSC, HBN) were analyzed separately. This choice was made so as to not mix data across MRI machine and MRI acquisition parameters. 随机化受试者未分组。每个队列（HCP、MSC、HBN）的数据分别进行分析。这样选择是为了不混合 MRI 机器和 MRI 采集参数的数据。
Blinding Data analysis was not performed blind to the conditions of the experiments. Blinding was not relevant because subjects were not evaluated based on group membership and blinding was not applicable to the whole-group analyses reported in this study. 数据分析未盲目进行，以符合实验条件。盲目性并不相关，因为受试者的评估并非基于组成员身份，而且盲目性并不适用于本研究中报告的整体组分析。
Reporting for specific materials, systems and methods 有关特定材料、系统和方法的报告
We require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material, system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response. 我们需要作者提供关于许多研究中使用的某些类型材料、实验系统和方法的信息。在这里，指出列出的每种材料、系统或方法是否与您的研究相关。如果您不确定列表项是否适用于您的研究，请在选择响应之前阅读相应部分。
Materials & experimental systems 材料和实验系统
Methods
Involved in the study 参与研究
Involved in the study 参与研究
Antibodies
ChIP-seq
凶
Eukaryotic cell lines 真核细胞系
区
Flow cytometry 流式细胞术
Palaeontology
[
MRI-based neuroimaging 基于 MRI 的神经影像学
Animals and other organisms 动物和其他生物
Human research participants 人类研究参与者
Clinical data 临床数据
Policy information about studies involving human research participants 有关涉及人类研究参与者的研究政策信息
Population characteristics The Human Connectome Project (HCP) aimed to collect healthy adult twins, ages 22-25 years old (Van Essen, 2012). The definition of "healthy" was broad, in order to collect a sample representative of the United States population in terms of behavior, ethnic, and socioeconomic diversity. In this study, a provided subset of subjects called the "Unrelated 100" was used. This subset has the following characteristics: female; mean age ; age range . 人口特征 人类连接组计划（HCP）旨在收集年龄在 22-25 岁之间的健康成年双胞胎（Van Essen，2012）。 “健康”的定义是广泛的，为了收集一个在行为、种族和社会经济多样性方面代表美国人口的样本。在这项研究中，使用了一个名为“不相关 100”的受试者子集。该子集具有以下特征：女性；平均年龄；年龄范围。
The Midnight Scan Club (MSC) consists of 10 participants who were healthy, right-handed, and aged 24-34 years old. Demographic information can be found in Gordon 2017, Table 1. 午夜扫描俱乐部（MSC）由 10 名健康、右撇子、年龄在 24-34 岁之间的参与者组成。人口统计信息可在 Gordon 2017 年的表 1 中找到。
The Healthy Brain Network Serial Scanning initiative (HBN) consists of 13 participants, aged 18-45 years old, who were used as pilot subjects for the wider Healthy Brain Network dataset collection (O'Connor 2017). Subject demographics can be found at: http://gigadb.org/dataset/100259 健康大脑网络连续扫描计划（HBN）由 13 名参与者组成，年龄在 18-45 岁之间，他们被用作更广泛的健康大脑网络数据集收集的试点对象（O'Connor 2017）。受试者人口统计信息可在以下网址找到：http://gigadb.org/dataset/100259
Recruitment 招募
HCP subjects were recruited from the Missouri Department of Health and Senior Services Bureau of Vital Records. MSC subjects were recruited from the Washington University in St. Louis community. HCP 受试者是从密苏里州卫生和老年服务局的重要记录局招募的。MSC 受试者是从圣路易斯华盛顿大学社区招募的。
HBN subjects were recruited from the community participating in the wider Healthy Brain Network project. These details can be found at: http://fcon_1000.projects.nitrc.org/indi/cmi_healthy_brain_network/Recruitement.html HBN 受试者是从更广泛的健康大脑网络项目参与社区招募的。这些详细信息可以在以下网址找到：http://fcon_1000.projects.nitrc.org/indi/cmi_healthy_brain_network/Recruitement.html
The authors of the present study did not collect any of the primary imaging data nor did they conduct recruitment of subjects. Therefore, the authors are not knowledgeable about possible self-section biases or other biases associated with the data collection of these three cohorts. Based on the previously described replications conducted on three independently acquired cohorts (across scanner strength as well), we would estimate that potential biases related to recruitment would not likely impact the main results of the study. 本研究的作者没有收集任何主要成像数据，也没有进行受试者招募。因此，作者对可能与这三个队列的数据收集相关的可能的自我选择偏见或其他偏见并不了解。基于先前描述的在三个独立获取的队列上进行的复制（跨扫描仪强度），我们估计与招募相关的潜在偏见不太可能影响研究的主要结果。
Ethics oversight 伦理监督
HCP was approved by the Washington University Institutional Review Board. HCP 已获得华盛顿大学机构审查委员会批准。
MSC was approved by Washington University School of Medicine Human Studies Committee and Institutional Review Board. HBN was approved by Chesapeake Institutional Review Board. MSC 已获得华盛顿大学医学院人类研究委员会和机构审查委员会批准。HBN 已获得切萨皮克机构审查委员会批准。
Note that full information on the approval of the study protocol must also be provided in the manuscript. 注意，研究方案获批的完整信息也必须在手稿中提供。
Magnetic resonance imaging 磁共振成像
Experimental design 实验设计
Design type 设计类型
Design specifications 设计规格
Behavioral performance measures 行为绩效指标
In this study, we used resting state scans (fixation cross, eyes open) and a movie watching task ("Raiders of the Lost Ark"). 在这项研究中，我们使用了静息态扫描（注视十字，眼睛睁开）和观看电影任务（《夺宝奇兵》）。
No blocks were used in this study 在这项研究中没有使用区块。
Behavioral measures were used were not used for the main findings of this study. In Supplementary Figures 21-23, we present an exploratory analysis on the relationship between EFC and principle components of behavioral scores in HCP subjects. Principal components analysis was performed on the following behavioral performance measures , which are available as HCP unrestricted measures: MMSE_Score, PSQI_Score, PSQI_Comp1, PSQI_Comp2, PSQI_Comp3, PSQI_Comp4, PSQI_Comp5, PSQI_Comp6, PSQI_Comp7, PSQI_Min2Asleep, PSQI_AmtSleep, PSQI_Latency30Min, PSQI_WakeUp, PSQI_Bathroom, PSQI_Breathe, PSQI_Snore, PSQI_TooCold, PSQI_TooHot, PSQI_BadDream, PSQI_Pain, PSQI_Other, PSQI_Quality, PSQI_SleepMeds, PSQI_DayStayAwake, PSQI_DayEnthusiasm, PSQI_BedPtnrRmate, PicSeq_Unadj, PicSeq_AgeAdj, CardSort_Unadj, CardSort_AgeAdj, Flanker_Unadj, Flanker_AgeAdj, PMAT24_A_CR, PMAT24_A_SI, PMAT24_A_RTCR, ReadEng_Unadj, ReadEng_AgeAdj, PicVocab_Unadj, PicVocab_AgeAdj, ProcSpeed_Unadj, ProcSpeed_AgeAdj, DDisc_SV_1mo_200, DDisc_SV_6mo_200, DDisc_SV_1yr_200, DDisc_SV_3yr_200, DDisc_SV_5yr_200, DDisc_SV_10yr_200, DDisc_SV_1mo_40K, DDisc_SV_6mo_40K, DDisc_SV_1yr_40K, DDisc_SV_3yr_40K, DDisc_SV_5yr_40K, DDisc_SV_10yr_40K, DDisc_AUC_200, DDisc_AUC_40K, VSPLOT_TC, VSPLOT_CRTE, VSPLOT_OOFF, SCPT_TP, SCPT_TN, SCPT_FP, SCPT_FN, SCPT_TPRT, SCPT_SEN, SCPT_SPEC, SCPT_LRNR, IWRD_TOT, IWRD_RTC, ListSort_Unadj, ListSort_AgeAdj, CogFluidComp_Unadj, CogFluidComp_AgeAdj, CogEarlyComp_Unadj, CogEarlyComp_AgeAdj, CogTotalComp_Unadj, CogTotalComp_AgeAdj, CogCrystalComp_Unadj, CogCrystalComp_AgeAdj, ER40_CR, ER40_CRT, ER4OANG, ER4OFEAR, ER4OHAP, ER4ONOE, ER4OSAD, AngAffect_Unadj, AngHostil_Unadj, AngAggr_Unadj, FearAffect_Unadj, FearSomat_Unadj, Sadness_Unadj, LifeSatisf_Unadj, MeanPurp_Unadj, PosAffect_Unadj, Friendship_Unadj, Loneliness_Unadj, PercHostil_Unadj, PercReject_Unadj, EmotSupp_Unadj, InstruSupp_Unadj, PercStress_Unadj, SelfEff_Unadj, Emotion_Task_Acc, Emotion_Task_Median_RT, Emotion_Task_Face_Acc, Emotion_Task_Face_Median_RT, Emotion_Task_Shape_Acc, Emotion_Task_Shape_Median_RT, Gambling_Task_Perc_Larger, Gambling_Task_Perc_Smaller, Gambling_Task_Median_RT_Larger, Gambling_Task_Reward_Perc_Larger, Gambling_Task_Reward_Median_RT_Larger, Gambling_Task_Reward_Perc_Smaller, Gambling_Task_Punish_Perc_Larger, 行为测量未用于本研究的主要发现。在补充图 21-23 中，我们对 HCP 受试者的 EFC 与行为分数主成分之间的关系进行了探索性分析。主成分分析是在以下行为表现指标上进行的，这些指标作为 HCP 无限制指标可用：MMSE 分数，PSQI 分数，PSQI_Comp1，PSQI_Comp2，PSQI_Comp3，PSQI_Comp4，PSQI_Comp5，PSQI_Comp6，PSQI_Comp7，PSQI_Min2Asleep，PSQI_AmtSleep，PSQI_Latency30Min，PSQI_WakeUp，PSQI_Bathroom，PSQI_Breathe，PSQI_Snore，PSQI_TooCold，PSQI_TooHot，PSQI_BadDream，PSQI_Pain，PSQI_Other，PSQI_Quality，PSQI_SleepMeds，PSQI_DayStayAwake，PSQI_DayEnthusiasm，PSQI_BedPtnrRmate，PicSeq_Unadj，PicSeq_AgeAdj，CardSort_Unadj，CardSort_AgeAdj，Flanker_Unadj，Flanker_AgeAdj，PMAT24_A_CR，PMAT24_A_SI，PMAT24_A_RTCR，ReadEng_Unadj，ReadEng_AgeAdj，PicVocab_Unadj，PicVocab_AgeAdj，ProcSpeed_Unadj，ProcSpeed_AgeAdj，DDisc_SV_1mo_200，DDisc_SV_6mo_200，DDisc_SV_1yr_200，DDisc_SV_3yr_200，DDisc_SV_5yr_200，DDisc_SV_10yr_200，DDisc_SV_1mo_40K，DDisc_SV_6mo_40K，DDisc_SV_1yr_40K，DDisc_SV_3yr_40K，DDisc_SV_5yr_40K，DDisc_SV_10yr_40K，DDisc_AUC_200，DDisc_AUC_40K，VSPLOT_TC，VSPLOT_CRTE，VSPLOT_OOFF，SCPT_TP，SCPT_TN，SCPT_FP，SCPT_FN，SCPT_TPRT，SCPT_SEN，SCPT_SPEC，SCPT_LRNR，IWRD_TOT，IWRD_RTC，ListSort_Unadj，ListSort_AgeAdj，CogFluidComp_UnadjComp_AgeAdj, CogEarlyComp_Unadj, CogEarlyComp_AgeAdj, CogTotalComp_Unadj, CogTotalComp_AgeAdj, CogCrystalComp_Unadj, CogCrystalComp_AgeAdj, ER40_CR, ER40_CRT, ER4OANG, ER4OFEAR, ER4OHAP, ER4ONOE, ER4OSAD, AngAffect_Unadj, AngHostil_Unadj, AngAggr_Unadj, FearAffect_Unadj, FearSomat_Unadj, Sadness_Unadj, LifeSatisf_Unadj, MeanPurp_Unadj, PosAffect_Unadj, Friendship_Unadj, Loneliness_Unadj, PercHostil_Unadj, PercReject_Unadj, EmotSupp_Unadj, InstruSupp_Unadj, PercStress_Unadj, SelfEff_Unadj, Emotion_Task_Acc, Emotion_Task_Median_RT, Emotion_Task_Face_Acc, Emotion_Task_Face_Median_RT, Emotion_Task_Shape_Acc, Emotion_Task_Shape_Median_RT, Gambling_Task_Perc_Larger, Gambling_Task_Perc_Smaller, Gambling_Task_Median_RT_Larger, Gambling_Task_Reward_Perc_Larger, Gambling_Task_Reward_Median_RT_Larger, Gambling_Task_Reward_Perc_Smaller, Gambling_Task_Punish_Perc_Larger,
Gambling_Task_Punish_Median_RT_Larger, Gambling_Task_Punish_Perc_Smaller, Language_Task_Acc, Language_Task_Median_RT, Language_Task_Story_Acc, Language_Task_Story_Median_RT, Language_Task_Story_Avg_Difficulty_Level, Language_Task_Math_Acc, Language_Task_Math_Median_RT, Language_Task_Math_Avg_Difficulty_Level, Relational_Task_Acc, Relational_Task_Median_RT, Relational_Task_Match_Acc, Relational_Task_Match_Median_RT, Relational_Task_Rel_Acc, Relational_Task_Rel_Median_RT, Social_Task_Perc_Random, Social_Task_Perc_TOM, Social_Task_Perc_Unsure, Social_Task_Median_RT_TOM, Social_Task_Random_Perc_Random, Social_Task_Random_Perc_TOM, Social_Task_Random_Perc_Unsure, Social_Task_TOM_Perc_Random, Social_Task_TOM_Perc_TOM, Social_Task_TOM_Médian_RT_TOM, Social_Task_TOM_Perc_Unsure, WM_Task_Acc, WM_Task_Median_RT, WM_Task_2bk_Acc, WM_Task_2bk_Median_RT, WM_Task_Obk_Acc, WM_Task_Obk_Median_RT, 赌博任务惩罚中位数反应时间较长，赌博任务惩罚百分比较小，语言任务准确率，语言任务中位数反应时间，语言任务故事准确率，语言任务故事中位数反应时间，语言任务故事平均难度级别，语言任务数学准确率，语言任务数学中位数反应时间，语言任务数学平均难度级别，关系任务准确率，关系任务中位数反应时间，关系任务匹配准确率，关系任务匹配中位数反应时间，关系任务关系准确率，关系任务关系中位数反应时间，社交任务随机百分比，社交任务 TOM 百分比，社交任务不确定百分比，社交任务 TOM 中位数反应时间，社交任务随机百分比随机，社交任务随机百分比 TOM，社交任务随机百分比不确定，社交任务 TOM 百分比随机，社交任务 TOM 百分比 TOM，社交任务 TOM 中位数反应时间 TOM，社交任务 TOM 百分比不确定，工作记忆任务准确率，工作记忆任务中位数反应时间，工作记忆任务 2bk 准确率，工作记忆任务 2bk 中位数反应时间，工作记忆任务 Obk 准确率，工作记忆任务 Obk 中位数反应时间
HCP: Resting state fMRI (rsfMRI) data was acquired with a gradient-echo EPI sequence (run duration = 14:33 min, TR = , flip angle degrees, isotropic voxel resolution, multiband factor ) with eyes open and instructions to fixate on a cross. Images were collected on a 3T Siemens Connectome Skyra with a 32-channel head coil. MSC: rsfMRI scans were collected with a gradient-echo EPI sequence (run duration , flip angle degrees, isotropic voxel resolution) with eyes open and with eye tracking recording to monitor for prolonged eye closure (to assess drowsiness). Images were collected on a 3T Siemens Trio. HCP：采用梯度回波 EPI 序列获取了静息态 fMRI（rsfMRI）数据（运行持续时间=14:33 分钟，TR= ，翻转角度 度， 等向体素分辨率，多带因子 ），眼睛睁开并被要求盯着十字。图像是在一台 3T 西门子 Connectome Skyra 上使用 32 通道头线圈收集的。MSC：采用梯度回波 EPI 序列获取了 rsfMRI 扫描（运行持续时间 ，翻转角度 度， 等向体素分辨率），眼睛睁开并使用眼动追踪记录以监测是否出现长时间闭眼（以评估嗜睡）。图像是在一台 3T 西门子 Trio 上收集的。
HBN: rsfMRI and movie watching (mvfMRI) were acquired with a gradient-echo EPI sequence (run duration rsfMRI = 10:18 min, per segment, , flip angle voxel resolution, multi-band factor ) with subjects instructed to keep their eyes open and gazed directed towards a cross during the rsMRI scan. Images were collected on a 1.5T Siemens Avanto with a 32-channel head coil. HBN：采用梯度回波 EPI 序列获取了静息态 fMRI 和观影（mvfMRI）数据（rsfMRI 运行持续时间=10:18 分钟，每段 ， ，翻转角度 体素分辨率，多带因子 ），被试验对象被要求在 rsMRI 扫描期间保持眼睛睁开并注视十字。图像是在一台 1.5T 西门子 Avanto 上使用 32 通道头线圈收集的。
whole-brain 整个大脑
Not used 未使用
Functional images in the HCP were processed with the HCP pipelines and downloaded after the 1200 subject data release. The HCP pipelines utilize FSL, Connectome Workbench, and custom MATLAB. Functional images in the MSC and HBN datasets were preprocessed using fMRIPrep 1.3.2 [90], which is based on Nipype 1.1.9 [91]. Internal operations of fMRIPrep use Nilearn 0.5.0, ANTs 2.2.0, FreeSurfer 6.0.1, FSL 5.0.9, and AFNI v16.2.07. For more details about the pipeline, see the section corresponding to workows in fMRIPrep's documentation, for version 1.3.2. HCP 中的功能图像使用 HCP pipelines 进行处理，并在 1200 个受试者数据发布后下载。HCP pipelines 利用 FSL、Connectome Workbench 和自定义 MATLAB。MSC 和 HBN 数据集中的功能图像使用基于 Nipype 1.1.9 的 fMRIPrep 1.3.2 [90] 进行预处理。fMRIPrep 的内部操作使用 Nilearn 0.5.0、ANTs 2.2.0、FreeSurfer 6.0.1、FSL 5.0.9 和 AFNI v16.2.07。有关管道的更多详细信息，请参阅 fMRIPrep 文档中与版本 1.3.2 对应的工作流程部分。
Within the fMRIPrep workflow, ANTs is used to align functional images to the MNI Asymmetrical template version 2009c. For HCP, FSL FNIRT is used to align functional images in the FSL MNI template and furthermore, multi-modal registration is used to align surface functional data to the fs_LR surface space. 在 fMRIPrep 工作流程中，使用 ANTs 将功能图像对齐到 MNI 非对称模板版本 2009c。对于 HCP，使用 FSL FNIRT 将功能图像对齐到 FSL MNI 模板，此外，使用多模态配准将表面功能数据对齐到 fs_LR 表面空间。
For HCP, fMRI data was analyzed after linear alignment (AC-PC) to the FSL MNI template. For MSC and HBN, fMRI data was analyzed in each subject's T1w space. 对于 HCP，fMRI 数据在线性对齐（AC-PC）到 FSL MNI 模板后进行分析。对于 MSC 和 HBN，fMRI 数据在每个受试者的 T1w 空间中进行分析。
We employed a 36-parameter nuisance regression strategy described Satterthwaite 2013 and shown to be an effective strategy in Parkes 2018. In Supplemental Figure 4, we present a scatter plot comparing eFC values derived from data processed with this 36-parameter strategy to eFC values derived from data processed with an ICA-FIX de-noising strategy. 我们采用了 Satterthwaite 2013 描述的 36 参数干扰回归策略，并证明在 Parkes 2018 中是一种有效策略。在补充图 4 中，我们呈现了一个散点图，比较使用这种 36 参数策略处理的数据得出的 eFC 值与使用 ICA-FIX 去噪策略处理的数据得出的 eFC 值。
We used spike regression in place of volume censoring. A spike regressor was added for each frame exceeding a motion threshold ( root mean squared displacement, framewise displacement) 我们在体积审查的位置使用了尖峰回归。为每个超过运动阈值的帧添加了一个尖峰回归器（ 均方根位移， 逐帧位移）
Specify type of analysis: 指定分析类型：
Statistic type for inference (See Eklund et al. 2016) 推断的统计类型（参见 Eklund 等人 2016 年）
Graph analysis 图分析
Voxel-wise or cluster-wise inference was not performed in this study. 本研究未进行基于体素或基于簇的推断。
In the comparison of rest versus movie eFC, we report nodes where eFC values significantly change based on a FDR (Benjamini-Hochberg) threshold alpha (Supplemental Figure 18). Furthmore, we employed a constrained null model to randomize edge values while presenting certain edge relationships (see Supplemental Figure 18). 在休息与电影 eFC 的比较中，我们报告了基于 FDR（Benjamini-Hochberg）阈值 alpha 显著变化的 eFC 值节点（见补充图 18）。此外，我们采用了一种受限的空模型来随机化边值，同时呈现特定的边关系（请参阅补充图 18）。
In this study, we propose a measure called eFC, which is conceptually related to Pearson correlation. The relation to Pearson correlation is explained in the manuscript. In Figure 1c, we compare eFC values to a multiplication of the edges' corresponding nFC values (Pearson correlation). We note that a direct comparison of eFC to nFC values is not possible, due to different data dimensionality. 在本研究中，我们提出了一种称为 eFC 的度量，概念上与 Pearson 相关性有关。与 Pearson 相关性的关系在手稿中有解释。在图 1c 中，我们将 eFC 值与边对应的 nFC 值（Pearson 相关性）的乘积进行了比较。我们注意到，由于数据维度不同，无法直接比较 eFC 和 nFC 值。
We construct an edge-by-edge graph (eFC matrix), which is weighted and undirected with entries from -1 to 1. These values represent the magnitude of co-fluctuation between edge time series. In this manuscript, we describe a method to apply community detection to this matrix. In Supplemental Figure 20, we provide examples of other network measures that can be applied to the eFC matrix and mapped back to the NxN space. 我们构建了一个边对边图（eFC 矩阵），其权重和方向均为 -1 到 1。这些值表示边时间序列之间共同波动的大小。在本手稿中，我们描述了一种将社区检测应用于该矩阵的方法。在补充图 20 中，我们提供了可以应用于 eFC 矩阵并映射回 NxN 空间的其他网络度量的示例。
'Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA. Program in Neuroscience, Indiana University, Bloomington, IN, USA. Cognitive Science Program, Indiana University, Bloomington, IN, USA. Network Science Institute, Indiana University, Bloomington, IN, USA.凶e-mail: rbetzel@indiana.edu 美国印第安纳大学布鲁明顿分校心理与脑科学系。美国印第安纳大学布鲁明顿分校神经科学项目。美国印第安纳大学布鲁明顿分校认知科学项目。美国印第安纳大学布鲁明顿分校网络科学研究所。邮箱：rbetzel@indiana.edu
