Community Finding: Partitioning Considered Harmful

Considering a clique as a conservative definition of community structure, we examine how partitioning algorithms interact with cliques. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across different partitions by popular algorithms. We examine the largest connected component of the subgraph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number of cliques split. We conclude that, due to the connectedness of many networks, any partitioning community finding algorithm must fail to return at least some significant structure. Moreover, contrary to traditional intuition, strong ties and cliques frequently do cross community boundaries.