Modularity of random intersection graphs

TL;DR

This paper investigates the effectiveness of modularity in detecting community structures within random intersection graphs, identifying parameter ranges where modularity succeeds or fails, and relating it to other graph models.

Contribution

It provides a detailed analysis of modularity's ability to detect communities in random intersection graphs and compares it with other models.

Findings

Modularity detects community structure in certain parameter ranges.

There are parameter ranges where community structure exists but is not detected by modularity.

The modularity of random intersection graphs is related to that of other known random graph models.

Abstract

Modularity was introduced by Newman and Girvan in 2004 and is used as a measure of community structure of networks represented by graphs. In our work we study modularity of the random intersection graph model first considered by Karo\'nski, Scheinerman, and Singer--Cohen in 1999. Since their introduction, random intersection graphs has attracted much attention, mostly due to their application as networks models. In our work we determine the range of parameters in which modularity detects well the community structure of the random intersection graphs, as well as give a range of parameters for which there is a community structure present but not revealed by modularity. We also relate modularity of the random intersection graph to the modularity of other known random graph models.