(a) The K
is not cohesive as a 3-clique community because it contains two 3-cliques (indicated by grey and white nodes) that do not share a node. However, it is a cohesive 4-, 5-, or 6-clique community. (b) The graph constitutes a 3- and a 4-clique community because the K6 (grey and white nodes) and the K5 (white and black nodes) share 3-nodes. However, the union of the two cliques contains 8 nodes, and thus it is not cohesive on both levels. For k = 3, the grey nodes build a K3, which does not share a node with the K3 built by the white nodes; for k = 4, the grey nodes and any of the white nodes build a K4, which does not share any node with the K4 built by the other 4 nodes.