## Results: 6

Figure 6. From: The development of Human Functional Brain Networks.

Figure 4. From: The development of Human Functional Brain Networks.

Figure 1. From: The development of Human Functional Brain Networks.

Figure 2. From: The development of Human Functional Brain Networks.

Figure 5. From: The development of Human Functional Brain Networks.

Figure 3. From: The development of Human Functional Brain Networks.

**adjacency matrix**of a model 22-node graph. For any two nodes, the value of the edge between them (here a 1 or 0), is found at the intersection of the respective row and column (or vice versa) of each node. For example, matrix entry (2,3) shows a value of 1, which is the edge between node 2 and node 3. (B) A

**spring-embedded layout**of the graph, where

**nodes**are circles, and

**edges**are lines between the nodes. (C) A list of several node properties. We illustrate several principles with this figure: the

**degree**of node 20 is 3, because it has 3 edges (to nodes 5, 16, and 22). These nodes are the

**neighbors**of node 20. The

**clustering coefficient**of this node is 0/3, since the neighbors share no edges, out of 3 possible edges. In contrast, the clustering coefficient of node 5 is 1/3. The

**minimum path length**is the number of edges that must be crossed to travel between two nodes. In the case of nodes 2 and 18 (red arrows), the minimum path length is 4 (2-3-6-22-18). The characteristic path length and average clustering coefficient are simply the average of all minimum path lengths and clustering coefficients across the network. The values of this network, in comparison to random and regular graphs, indicate a small-world structure. The

**betweenness centrality**of a node is (proportional to) the fraction of all shortest paths in the network that run through the node. The value for node 1 is 0, whereas the values for nodes 6 and 22 are among the highest in the network, since paths from green to blue nodes almost always use these nodes. High degree and betweenness centrality values are often used to identify

**hubs**, but these values do not necessarily correlate with each other, and must be used with caution, as illustrated by comparing the properties of node 2 with node 18 (values circled in red). Node 2 has a relatively high betweenness centrality, despite the fact that it is evidently not playing a “central” role in the network. This “discrepancy” is because all shortest paths to node 1 must traverse node 2, inflating its betweenness centrality. Contrast the network position of node 2 with that of node 18, which has a much higher degree but only slightly higher betweenness centrality, or node 9, which has high degree but quite low betweenness centrality.

**Community structure**is visually evident in this layout, and modularity-optimizing algorithms obtain the partition indicated by node colorings, which yields a “modularity” of 0.54. Modularity values above 0.3 are typically thought to indicate strong community structure.