Hierarchical configuration model

Research output: Contribution to journalArticleAcademicpeer-review

88 Downloads (Pure)

Abstract

We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the configuration model is replaced by a community: i.e., a small graph. These communities may have any shape, as long as they are connected. For these hierarchical graphs, we find the size of the largest component, the degree distribution and the clustering coefficient.
Furthermore, we determine the conditions under which a giant percolation cluster exists, and find its size.
Original languageEnglish
Article number1214
Number of pages25
JournalInternet Mathematics
DOIs
Publication statusPublished - 30 Dec 2016

Fingerprint

Configuration
Graph in graph theory
Clustering Coefficient
Community Structure
Degree Distribution
Random Graphs
Model
Community
Vertex of a graph
Class

Cite this

@article{73d791ca4fe94d5fad4eb43f25e66b79,
title = "Hierarchical configuration model",
abstract = "We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the configuration model is replaced by a community: i.e., a small graph. These communities may have any shape, as long as they are connected. For these hierarchical graphs, we find the size of the largest component, the degree distribution and the clustering coefficient.Furthermore, we determine the conditions under which a giant percolation cluster exists, and find its size.",
author = "{van der Hofstad}, R. and {van Leeuwaarden}, J.S.H. and C. Stegehuis",
year = "2016",
month = "12",
day = "30",
doi = "10.24166/im.01.2017",
language = "English",
journal = "Internet Mathematics",
issn = "1542-7951",
publisher = "Taylor and Francis Ltd.",

}

Hierarchical configuration model. / van der Hofstad, R.; van Leeuwaarden, J.S.H.; Stegehuis, C.

In: Internet Mathematics, 30.12.2016.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Hierarchical configuration model

AU - van der Hofstad, R.

AU - van Leeuwaarden, J.S.H.

AU - Stegehuis, C.

PY - 2016/12/30

Y1 - 2016/12/30

N2 - We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the configuration model is replaced by a community: i.e., a small graph. These communities may have any shape, as long as they are connected. For these hierarchical graphs, we find the size of the largest component, the degree distribution and the clustering coefficient.Furthermore, we determine the conditions under which a giant percolation cluster exists, and find its size.

AB - We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the configuration model is replaced by a community: i.e., a small graph. These communities may have any shape, as long as they are connected. For these hierarchical graphs, we find the size of the largest component, the degree distribution and the clustering coefficient.Furthermore, we determine the conditions under which a giant percolation cluster exists, and find its size.

U2 - 10.24166/im.01.2017

DO - 10.24166/im.01.2017

M3 - Article

JO - Internet Mathematics

JF - Internet Mathematics

SN - 1542-7951

M1 - 1214

ER -