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.

On sparsity, power-law, and clustering properties of graphex processes / Caron, François; Panero, Francesca; Rousseau, Judith. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - 55:4(2023), pp. 1211-1253. [10.1017/apr.2022.75]

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

Francesca Panero;
2023

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.
2023
community structure; generalised graphon; networks; poisson processes; power law; sparsity; subgraph counts; transitivity
01 Pubblicazione su rivista::01a Articolo in rivista
On sparsity, power-law, and clustering properties of graphex processes / Caron, François; Panero, Francesca; Rousseau, Judith. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - 55:4(2023), pp. 1211-1253. [10.1017/apr.2022.75]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1711674
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