On sparsity, power-law, and clustering properties of graphex processes

Caron, François, Panero, Francesca ORCID: 0000-0002-8287-163X and Rousseau, Judith (2023) On sparsity, power-law, and clustering properties of graphex processes. Advances in Applied Probability. ISSN 0001-8678

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Abstract

This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes, and degree distributions, identifying four regimes: (i) a dense regime, (ii) a sparse, almost dense regime, (iii) a sparse regime with power-law behaviour, and (iv) an almost extremely sparse regime. We show that, under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same. We also derive a central limit theorem for subgraph counts and for the number of nodes. Finally, we propose a class of models within this framework where one can separately control the latent structure and the global sparsity/power-law properties of the graph.

Item Type:	Article
Additional Information:	© 2023 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Date Deposited:	21 Jul 2023 11:06
Last Modified:	25 Apr 2024 20:06
URI:	http://eprints.lse.ac.uk/id/eprint/119794

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