  One of the most remarkable social phenomena is the formation of communities
in social networks corresponding to families, friendship circles, work teams,
etc. Since people usually belong to several different communities at the same
time, the induced overlaps result in an extremely complicated web of the
communities themselves. Thus, uncovering the intricate community structure of
social networks is a non-trivial task with great potential for practical
applications, gaining a notable interest in the recent years. The Clique
Percolation Method (CPM) is one of the earliest overlapping community finding
methods, which was already used in the analysis of several different social
networks. In this approach the communities correspond to k-clique percolation
clusters, and the general heuristic for setting the parameters of the method is
to tune the system just below the critical point of k-clique percolation.
However, this rule is based on simple physical principles and its validity was
never subject to quantitative analysis. Here we examine the quality of the
partitioning in the vicinity of the critical point using recently introduced
overlapping modularity measures. According to our results on real social- and
other networks, the overlapping modularities show a maximum close to the
critical point, justifying the original criteria for the optimal parameter
settings.
