Clique percolation method: memory efficient almost exact communities

TL;DR

This paper enhances the clique percolation method for community detection in large graphs by improving scalability and memory efficiency, introducing a near-exact alternative algorithm for cases with memory constraints.

Contribution

It extends the clique percolation method to large graphs, offering a scalable exact algorithm and a memory-efficient approximate algorithm for community detection.

Findings

Scalable algorithm for listing all k-cliques in large graphs.

Memory-efficient approximate algorithm CPMZ.

Effective community detection in large real-world graphs.

Abstract

Automatic detection of relevant groups of nodes in large real-world graphs, i.e. community detection, has applications in many fields and has received a lot of attention in the last twenty years. The most popular method designed to find overlapping communities (where a node can belong to several communities) is perhaps the clique percolation method (CPM). This method formalizes the notion of community as a maximal union of $k$-cliques that can be reached from each other through a series of adjacent $k$-cliques, where two cliques are adjacent if and only if they overlap on $k-1$ nodes. Despite much effort CPM has not been scalable to large graphs for medium values of $k$. Recent work has shown that it is possible to efficiently list all $k$-cliques in very large real-world graphs for medium values of $k$. We build on top of this work and scale up CPM. In cases where this first algorithm faces memory limitations, we propose another algorithm, CPMZ, that provides a solution close to the exact one, using more time but less memory.