Detection of node group membership in networks with group overlap

TL;DR

This paper introduces an ensemble of networks with overlapping communities and evaluates three detection methods, finding that modularity-landscape surveying uniquely detects overlapping node memberships, especially when overlaps are small.

Contribution

It provides a formal framework and testing environment for detecting overlapping communities, highlighting the effectiveness of modularity-landscape surveying over other methods.

Findings

Modularity-landscape surveying detects heterogeneities in node memberships.

Detection of overlaps is only effective when overlaps are small.

k-clique percolation fails to detect overlapping node memberships.

Abstract

Most networks found in social and biochemical systems have modular structures. An important question prompted by the modularity of these networks is whether nodes can be said to belong to a single group. If they cannot, we would need to consider the role of "overlapping communities." Despite some efforts in this direction, the problem of detecting overlapping groups remains unsolved because there is neither a formal definition of overlapping community, nor an ensemble of networks with which to test the performance of group detection algorithms when nodes can belong to more than one group. Here, we introduce an ensemble of networks with overlapping groups. We then apply three group identification methods--modularity maximization, k-clique percolation, and modularity-landscape surveying--to these networks. We find that the modularity-landscape surveying method is the only one able to detect heterogeneities in node memberships, and that those heterogeneities are only detectable when the overlap is small. Surprisingly, we find that the k-clique percolation method is unable to detect node membership for the overlapping case.