Clustering and percolation on superpositions of Bernoulli random graphs

A simple but powerful network model with n$$ n $$ nodes and m$$ m $$ partly overlapping layers is generated as an overlay of independent random graphs G1,…,Gm$$ {G}_1,\dots, {G}_m $$ with variable sizes and densities. The model is parameterized by a joint distribution Pn$$ {P}_n $$ of layer sizes an...

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Bibliographic Details
Published in:Random structures & algorithms Vol. 63; no. 2; pp. 283 - 342
Main Authors: Bloznelis, Mindaugas, Leskelä, Lasse
Format: Journal Article
Language:English
Published: New York John Wiley & Sons, Inc 01.09.2023
Wiley Subscription Services, Inc
Subjects:
bond percolation
Clustering
clustering coefficient
complex network
giant component
Graphs
intersection graph
Overlapping communities
Percolation
Phase transitions
power law
random graph
site percolation
ISSN:1042-9832, 1098-2418
Online Access:Get full text
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Summary:A simple but powerful network model with n$$ n $$ nodes and m$$ m $$ partly overlapping layers is generated as an overlay of independent random graphs G1,…,Gm$$ {G}_1,\dots, {G}_m $$ with variable sizes and densities. The model is parameterized by a joint distribution Pn$$ {P}_n $$ of layer sizes and densities. When m$$ m $$ grows linearly and Pn→P$$ {P}_n\to P $$ as n→∞$$ n\to \infty $$, the model generates sparse random graphs with a rich statistical structure, admitting a nonvanishing clustering coefficient together with a limiting degree distribution and clustering spectrum with tunable power‐law exponents. Remarkably, the model admits parameter regimes in which bond percolation exhibits two phase transitions: the first related to the emergence of a giant connected component, and the second to the appearance of gigantic single‐layer components.
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.21140