Canonical labeling of subgraph structures. 2A: The columns of the adjacency matrix are arranged according to the natural order of node labels. As this is a complete graph, there are edges between every pair of distinct nodes. Therefore non-diagonal elements are all 1. And since there is no self-loop in the graph, the diagonal elements are all 0. The canonical label [V1, V2, V3, V4]0111011010 is formed of two parts. The first part [V1, V2, V3, V4] is the concatenation of node labels, delimited by comma. The second part 0111011010 is the concatenation of upper triangle of adjacency matrix. Two parts are separated by square bracket. 2B: Three of the nodes are having same cluster ID, which results in three possible adjacency matrices to be constructed.
Shen et al. BMC Systems Biology 2012 6(Suppl 3):S2 doi:10.1186/1752-0509-6-S3-S2