Community Detection in Networks using Graph Distance

TL;DR

This paper introduces a graph-distance-based algorithm for community detection in networks, providing theoretical guarantees for various models and demonstrating promising results on real-world networks.

Contribution

It proposes a novel community detection algorithm with theoretical guarantees for sparse and complex networks, extending to degree-corrected and growing community models.

Findings

The algorithm successfully identifies communities in block models.

Theoretical guarantees are established for various network models.

Favorable simulation results on real-world networks.

Abstract

The study of networks has received increased attention recently not only from the social sciences and statistics but also from physicists, computer scientists and mathematicians. One of the principal problem in networks is community detection. Many algorithms have been proposed for community finding but most of them do not have have theoretical guarantee for sparse networks and networks close to the phase transition boundary proposed by physicists. There are some exceptions but all have some incomplete theoretical basis. Here we propose an algorithm based on the graph distance of vertices in the network. We give theoretical guarantees that our method works in identifying communities for block models and can be extended for degree-corrected block models and block models with the number of communities growing with number of vertices. Despite favorable simulation results, we are not yet able to conclude that our method is satisfactory for worst possible case. We illustrate on a network of political blogs, Facebook networks and some other networks.