Percolation Computation in Complex Networks

TL;DR

This paper explores the computational challenges of k-clique percolation in complex networks, proposing improved algorithms that enable analysis of larger datasets despite the problem's inherent complexity.

Contribution

It introduces a simple, improved algorithm for k-clique percolation and demonstrates its effectiveness on large empirical networks with overlapping communities.

Findings

Improved algorithm performs better on large datasets.

Higher k values still pose computational challenges.

Clique percolation remains computationally hard.

Abstract

K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using clique graphs, certain aspects of k-clique percolation are computationally challenging in practice. In this paper we investigate aspects of empirical social networks, such as the large numbers of overlapping maximal cliques contained within them, that make clique percolation, and clique graph representations, computationally expensive. We motivate a simple algorithm to conduct clique percolation, and investigate its performance compared to current best-in-class algorithms. We present improvements to this algorithm, which allow us to perform k-clique percolation on much larger empirical datasets. Our approaches perform much better than existing algorithms on networks exhibiting pervasively overlapping community structure, especially for higher values of k. However, clique percolation remains a hard computational problem; current algorithms still scale worse than some other overlapping community finding algorithms.