Degree correlations in graphs with clique clustering

Peter Stephen Mann; V.A. Smith; John B. O. Mitchell; Simon Andrew Dobson

doi:10.1103/PhysRevE.105.044314

Degree correlations in graphs with clique clustering

Peter Stephen Mann^*, V.A. Smith, John B. O. Mitchell, Simon Andrew Dobson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.

Original language	English
Article number	044314
Number of pages	14
Journal	Physical Review. E, Statistical, nonlinear, and soft matter physics
Volume	105
Issue number	4
Early online date	20 Apr 2022
DOIs	https://doi.org/10.1103/PhysRevE.105.044314
Publication status	Published - 30 Apr 2022

Keywords

Complex networks
Clustering

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10.1103/PhysRevE.105.044314

Mann-2022-Degree-correlations-in-graphs-PhysRevE-AAM
Copyright © 2022 American Physical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1103/PhysRevE.105.044314.
Accepted author manuscript, 0.98 MB

Science of Sensor System Software: Science of Sensor System Software
Dobson, S. (PI)
EPSRC
1/01/16 → 31/12/22
Project: Standard

Cite this

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title = "Degree correlations in graphs with clique clustering",

abstract = "Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.",

keywords = "Complex networks, Clustering",

author = "Mann, {Peter Stephen} and V.A. Smith and Mitchell, {John B. O.} and Dobson, {Simon Andrew}",

note = "Funding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).",

year = "2022",

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doi = "10.1103/PhysRevE.105.044314",

language = "English",

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T1 - Degree correlations in graphs with clique clustering

AU - Mann, Peter Stephen

AU - Smith, V.A.

AU - Mitchell, John B. O.

AU - Dobson, Simon Andrew

N1 - Funding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).

PY - 2022/4/30

Y1 - 2022/4/30

N2 - Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.

AB - Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.

KW - Complex networks

KW - Clustering

U2 - 10.1103/PhysRevE.105.044314

DO - 10.1103/PhysRevE.105.044314

M3 - Article

SN - 1539-3755

VL - 105

JO - Physical Review. E, Statistical, nonlinear, and soft matter physics

JF - Physical Review. E, Statistical, nonlinear, and soft matter physics

IS - 4

M1 - 044314

ER -

Degree correlations in graphs with clique clustering

Abstract

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Science of Sensor System Software: Science of Sensor System Software

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