Core–satellite graphs: clustering, assortativity and spectral properties

Ernesto Estrada, Michele Benzi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average Watts-Strogatz clustering coefficient and the transitivity index, diverge when the graph size increases. We also show that these graphs are disassortative. In addition, we completely describe the spectrum of the adjacency and Laplacian matrices associated with core-satellite graphs. Finally, we introduce the class of generalized core-satellite graphs and analyze their clustering, assortativity, and spectral properties.
LanguageEnglish
Pages30-52
Number of pages23
JournalLinear Algebra and its Applications
Volume517
Early online date8 Dec 2016
DOIs
Publication statusPublished - 15 Mar 2017

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Graph Clustering
Spectral Properties
Satellites
Graph in graph theory
Clustering
Laplacian Matrix
Clustering Coefficient
Transitivity
Adjacency Matrix
Diverge
Generalise

Keywords

  • generalized core-satellite graphs
  • transivity index
  • average Watts-Strogatz
  • clustering coefficient
  • graph spectra
  • Laplacian spectra

Cite this

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Core–satellite graphs : clustering, assortativity and spectral properties. / Estrada, Ernesto; Benzi, Michele.

In: Linear Algebra and its Applications, Vol. 517, 15.03.2017, p. 30-52.

Research output: Contribution to journalArticle

TY - JOUR

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T2 - Linear Algebra and its Applications

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AU - Benzi, Michele

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AB - Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average Watts-Strogatz clustering coefficient and the transitivity index, diverge when the graph size increases. We also show that these graphs are disassortative. In addition, we completely describe the spectrum of the adjacency and Laplacian matrices associated with core-satellite graphs. Finally, we introduce the class of generalized core-satellite graphs and analyze their clustering, assortativity, and spectral properties.

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