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Exploring network structure with the density of states

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  • Arthur, Rudy

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 which suggests 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.

Suggested Citation

  • Arthur, Rudy, 2025. "Exploring network structure with the density of states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
    • Handle: RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125003942
    DOI: 10.1016/j.physa.2025.130742
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    References listed on IDEAS

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    1. Atsushi Miyauchi & Yasushi Kawase, 2016. "Z-Score-Based Modularity for Community Detection in Networks," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-17, January.
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    4. Arthur, Rudy, 2023. "Discovering block structure in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
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    6. Arthur, Rudy, 2020. "Modularity and projection of bipartite networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    7. Rodrigo Aldecoa & Ignacio Marín, 2011. "Deciphering Network Community Structure by Surprise," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-8, September.
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