Exploring Network Structure with the Density of States

TL;DR

This paper introduces the density of states as a novel tool for analyzing the entire space of network partitions, helping to identify meaningful structures and avoid spurious findings in community detection.

Contribution

It presents a new application of the Wang-Landau method to compute the density of states, enabling exploration of all possible network partitions rather than just optimal ones.

Findings

Density of states can distinguish true structures from random noise.

Method overcomes resolution limits in community detection.

Identifies consistent node groups across partitions.

Abstract

Community detection, as well as the identification of other structures like core periphery and disassortative patterns, is an important topic in network analysis. While most methods seek to find the best partition of the network according to some criteria, there is a body of results that suggest that a single network can have many good but distinct partitions. In this paper we introduce the density of states as a tool for studying the space of all possible network partitions. We demonstrate how to use the well known Wang-Landau method to compute a network's density of states. We show that, even using modularity to measure quality, the density of states can still rule out spurious structure in random networks and overcome resolution limits. We demonstrate how these methods can be used to find `building blocks', groups of nodes which are consistently found together in detected communities. This suggests an approach to partitioning based on exploration of the network's structure landscape rather than optimisation.