Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs

A. J. E. M. Janssen, Johan S. H. van Leeuwaarden, Seva Shneer

Research output: Contribution to journalArticle

Abstract

Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral expressions amenable to asymptotic analysis. We obtain various asymptotic descriptions for how the average number of cliques and cycles, of any size, grow with the network size. For the cycle asymptotics we invoke the theory of circulant matrices.
Original languageEnglish
Pages (from-to)161-184
Number of pages24
JournalJournal of Statistical Physics
Volume175
Issue number1
Early online date18 Feb 2019
DOIs
Publication statusPublished - Apr 2019

Fingerprint

Clique
Random Graphs
Counting
Cycle
Infinite Variance
Circulant Matrix
Scale-free Networks
Asymptotic Analysis
Model

Keywords

  • Cliques
  • Power-law distributions
  • Random graphs
  • Scale-free networks
  • Subgraphs

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Janssen, A. J. E. M. ; van Leeuwaarden, Johan S. H. ; Shneer, Seva. / Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs. In: Journal of Statistical Physics. 2019 ; Vol. 175, No. 1. pp. 161-184.
@article{ee2a03013d1c46bd8e73b82430cc0162,
title = "Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs",
abstract = "Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral expressions amenable to asymptotic analysis. We obtain various asymptotic descriptions for how the average number of cliques and cycles, of any size, grow with the network size. For the cycle asymptotics we invoke the theory of circulant matrices.",
keywords = "Cliques, Power-law distributions, Random graphs, Scale-free networks, Subgraphs",
author = "Janssen, {A. J. E. M.} and {van Leeuwaarden}, {Johan S. H.} and Seva Shneer",
year = "2019",
month = "4",
doi = "10.1007/s10955-019-02248-w",
language = "English",
volume = "175",
pages = "161--184",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer",
number = "1",

}

Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs. / Janssen, A. J. E. M.; van Leeuwaarden, Johan S. H.; Shneer, Seva.

In: Journal of Statistical Physics, Vol. 175, No. 1, 04.2019, p. 161-184.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Counting Cliques and Cycles in Scale-Free Inhomogeneous Random Graphs

AU - Janssen, A. J. E. M.

AU - van Leeuwaarden, Johan S. H.

AU - Shneer, Seva

PY - 2019/4

Y1 - 2019/4

N2 - Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral expressions amenable to asymptotic analysis. We obtain various asymptotic descriptions for how the average number of cliques and cycles, of any size, grow with the network size. For the cycle asymptotics we invoke the theory of circulant matrices.

AB - Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral expressions amenable to asymptotic analysis. We obtain various asymptotic descriptions for how the average number of cliques and cycles, of any size, grow with the network size. For the cycle asymptotics we invoke the theory of circulant matrices.

KW - Cliques

KW - Power-law distributions

KW - Random graphs

KW - Scale-free networks

KW - Subgraphs

UR - http://www.scopus.com/inward/record.url?scp=85061721289&partnerID=8YFLogxK

U2 - 10.1007/s10955-019-02248-w

DO - 10.1007/s10955-019-02248-w

M3 - Article

VL - 175

SP - 161

EP - 184

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -