Figure 8

(a) This graph consists of three maximal cliques: (1, 2, 3, 4), (4, 5, 6), and (4, 5, 6, 7). The 3-clique community on level 3 is not cohesive because there are two 3-cliques, namely (1, 2, 3) and (5, 6, 7), indicated by red, bold edges, that do not share a node. An equivalent argumentation is that the union of (1, 2, 3, 4) and (4, 5, 6, 7) contains 7 distinct nodes, i.e., more than 2k = 6 nodes. Both 4-clique communities are cohesive because they consist of a single clique with size less than 2k = 8. (b) This graph consists of a two maximal cliques: (1, 2, 3, 4, 5) and (3, 4, 5, 6, 7). On both levels, 3 and 4, the k-clique community consists of both cliques, but on level 3 the 3-clique community is not cohesive because (1, 2, 3) and (5, 6, 7) still share no single node. But on level 4 the 4-clique community is cohesive because the union of the two maximal cliques contains 7, i.e., less than 2k = 8 nodes.