Example of block adjacency matrix for a network describing the behavior of two interacting communities.

<p>Any adjacency matrix can be represented as a block matrix with a vertex permutation that groups nodes depending on the cluster to which they belong (i.e., first those belonging to cluster 1 - - and then those related to cluster 2 - - or vice versa). Specifically, blocks on the main diagonal refer to within-cluster connections while off-diagonal blocks contain between cluster connections. In particular, the block refers to between-cluster connections from cluster to cluster . The legend of colors links the number of nonzero elements (i.e., the number of exiting links) in each block to the corresponding expression according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0319031#pone.0319031.e295" target="_blank">Eqs. 38</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0319031#pone.0319031.e301" target="_blank">44</a>.</p>