Estimating the number of communities in a network

TL;DR

This paper introduces a maximum-likelihood method for accurately determining the number of communities in a network, addressing a key challenge in community detection.

Contribution

It presents a mathematically principled approach to estimate the optimal number of communities, validated on real-world networks with known structures.

Findings

Successfully determines the number of communities in all tested real-world networks

Provides a rigorous statistical framework for community number estimation

Outperforms heuristic methods in accuracy

Abstract

Community detection, the division of a network into dense subnetworks with only sparse connections between them, has been a topic of vigorous study in recent years. However, while there exist a range of powerful and flexible methods for dividing a network into a specified number of communities, it is an open question how to determine exactly how many communities one should use. Here we describe a mathematically principled approach for finding the number of communities in a network using a maximum-likelihood method. We demonstrate the approach on a range of real-world examples with known community structure, finding that it is able to determine the number of communities correctly in every case.