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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Vydané v:Random structures & algorithms Ročník 63; číslo 2; s. 283 - 342
Hlavní autori: Bloznelis, Mindaugas, Leskelä, Lasse
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York John Wiley & Sons, Inc 01.09.2023
Wiley Subscription Services, Inc
Predmet:
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
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Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.21140