Statistical complexity of heterogeneous geometric networks

Smith, KM and Smith, JP ORCID: https://orcid.org/0000-0002-4209-1604, 2025. Statistical complexity of heterogeneous geometric networks. PLOS Complex Systems, 2 (1), e0000026. ISSN 2837-8830

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Abstract

Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical complexity of networks is not well understood. We introduce a parsimonious normalised measure of statistical complexity for networks. The measure is trivially 0 in regular graphs and we prove that this measure tends to 0 in Erdös-Rényi random graphs in the thermodynamic limit. We go on to demonstrate that greater complexity arises from the combination of heterogeneous and geometric components to the network structure than either on their own. Further, the levels of complexity achieved are similar to those found in many real-world networks. However, we also find that real-world networks establish connections in a way which increases complexity and which our null models fail to explain. We study this using ten link growth mechanisms and find that only one mechanism successfully and consistently replicates this phenomenon– probabilities proportional to the exponential of the number of common neighbours between two nodes. Common neighbours is a mechanism which implicitly accounts for degree heterogeneity and latent geometry. This explains how a simple mechanism facilitates the growth of statistical complexity in real-world networks.

Item Type:	Journal article
Publication Title:	PLOS Complex Systems
Creators:	Smith, K.M. and Smith, J.P.
Publisher:	Public Library of Science
Date:	3 January 2025
Volume:	2
Number:	1
ISSN:	2837-8830
Identifiers:	Number Type 10.1371/journal.pcsy.0000026 DOI 2333276 Other
Rights:	© 2025 Smith, Smith. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Divisions:	Schools > School of Science and Technology
Record created by:	Jonathan Gallacher
Date Added:	09 Jan 2025 09:44
Last Modified:	09 Jan 2025 09:53
URI:	https://irep.ntu.ac.uk/id/eprint/52824

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