Finding Maximum Cliques in Large Networks

TL;DR

This paper introduces a graph reduction technique that efficiently finds maximum cliques in large networks by reducing graph size, demonstrated on social and random graphs.

Contribution

The paper presents a novel graph reduction method that enables maximum clique detection in large graphs where traditional methods are infeasible.

Findings

Effective reduction of graph size for maximum clique detection

Application to real-world social networks

Validation on Erdős-Rényi random graphs

Abstract

There are many methods to find a maximum (or maximal) clique in large networks. Due to the nature of combinatorics, computation becomes exponentially expensive as the number of vertices in a graph increases. Thus, there is a need for efficient algorithms to find a maximum clique. In this paper, we present a graph reduction method that significantly reduces the order of a graph, and so enables the identification of a maximum clique in graphs of large order, that would otherwise be computational infeasible to find the maximum. We find bounds of the maximum (or maximal) clique using this reduction. We demonstrate our method on real-life social networks and also on Erd\"{o}s-Renyi random graphs.