Overlapping modularity at the critical point of k-clique percolation

TL;DR

This paper investigates the optimal parameter setting for the Clique Percolation Method in social network analysis by analyzing overlapping modularity measures near the critical point of k-clique percolation, confirming the heuristic's validity.

Contribution

It provides a quantitative analysis of the critical point in k-clique percolation, validating the heuristic for parameter tuning using overlapping modularity measures.

Findings

Overlapping modularity peaks near the critical point of k-clique percolation.

The heuristic for parameter tuning is justified by the modularity analysis.

Results are consistent across real social and other networks.

Abstract

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.