fraction of total number of edges in the network to the total number of possible edges: . Finally, betweenness centrality is the sum of all the shortest paths that pass through the node of interest weighted by the inverse of the total number of shortest paths between two nodes: , where ρhj is the shortest path or the fewest number of edges that can be traversed between two nodes. For simplicity, we averaged the betweenness centrality across hemispheres (Fig. 2D and Fig. 4D,E).
