Clique and cycle frequencies in a sparse random graph model with overlapping communities

Fuente: arXiv
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Main Authors: Gröhn, Tommi, Karjalainen, Joona, Leskelä, Lasse
Format: Preprint
Published: 2019
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author Gröhn, Tommi
Karjalainen, Joona
Leskelä, Lasse
author_facet Gröhn, Tommi
Karjalainen, Joona
Leskelä, Lasse
contents A statistical network model with overlapping communities can be generated as a superposition of mutually independent random graphs of varying size. The model is parameterized by the number of nodes, the number of communities, and the joint distribution of the community size and the edge probability. This model admits sparse parameter regimes with power-law limiting degree distributions and non-vanishing clustering coefficients. This article presents large-scale approximations of clique and cycle frequencies for graph samples generated by the model, which are valid for regimes with unbounded numbers of overlapping communities. Our results reveal the growth rates of these subgraph frequencies and show that their theoretical densities can be reliably estimated from data.
format Preprint
id arxiv_https___arxiv_org_abs_1911_12827
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle Clique and cycle frequencies in a sparse random graph model with overlapping communities
Gröhn, Tommi
Karjalainen, Joona
Leskelä, Lasse
Probability
Social and Information Networks
Statistics Theory
62F10, 05C80, 60C05
A statistical network model with overlapping communities can be generated as a superposition of mutually independent random graphs of varying size. The model is parameterized by the number of nodes, the number of communities, and the joint distribution of the community size and the edge probability. This model admits sparse parameter regimes with power-law limiting degree distributions and non-vanishing clustering coefficients. This article presents large-scale approximations of clique and cycle frequencies for graph samples generated by the model, which are valid for regimes with unbounded numbers of overlapping communities. Our results reveal the growth rates of these subgraph frequencies and show that their theoretical densities can be reliably estimated from data.
title Clique and cycle frequencies in a sparse random graph model with overlapping communities
topic Probability
Social and Information Networks
Statistics Theory
62F10, 05C80, 60C05
url https://arxiv.org/abs/1911.12827