Listing All Maximal Cliques in Large Sparse Real-World Graphs

TL;DR

This paper presents a practical algorithm for listing all maximal cliques in large sparse real-world graphs, outperforming previous methods in efficiency and memory usage, enabling analysis of massive graphs.

Contribution

The paper introduces a new algorithm based on Eppstein, L"offler, and Strash's work that is efficient for large sparse graphs and overcomes memory limitations of prior algorithms.

Findings

The new algorithm is the first practical solution for large sparse graphs.

It outperforms existing algorithms in speed on real-world data.

It requires less memory, enabling analysis of larger graphs.

Abstract

We implement a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, L\"offler, and Strash (ISAAC 2010) and analyze its performance on a large corpus of real-world graphs. Our analysis shows that this algorithm is the first to offer a practical solution to listing all maximal cliques in large sparse graphs. All other theoretically-fast algorithms for sparse graphs have been shown to be significantly slower than the algorithm of Tomita et al. (Theoretical Computer Science, 2006) in practice. However, the algorithm of Tomita et al. uses an adjacency matrix, which requires too much space for large sparse graphs. Our new algorithm opens the door for fast analysis of large sparse graphs whose adjacency matrix will not fit into working memory.