Communities for our graph were detected with the modularity optimization method of Newman [46]. The modularity, or Q, of a graph is a quantitative measure of the number of edges found within communities versus the number predicted in a random graph with equivalent degree distribution. A positive Q indicates that the number of intra-community edges exceeds those predicted statistically. A wide range of Q may be found for a graph, depending on how nodes are assigned to communities. The set of node assignments that returns the highest Q is the optimal community structure sought by the modularity optimization algorithm, which follows a recursive two-step process. First, a modularity matrix similar to a Laplacian is constructed from the nodes in question, comparing observed versus expected edges. If this matrix has a positive eigenvalue, the eigenvector of the largest eigenvalue is used to split the nodes into two subgraphs, and Q is calculated. Second, nodes are swapped individually between the two subgraphs to see if an increase in Q can be found. Once a maximal Q is found from these swaps, the
