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June 2013 Degree and clustering coefficient in sparse random intersection graphs
Mindaugas Bloznelis
Ann. Appl. Probab. 23(3): 1254-1289 (June 2013). DOI: 10.1214/12-AAP874

Abstract

We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129–132]. For sparse graphs with a positive clustering coefficient, we examine statistical dependence between the (local) clustering coefficient and the degree. Our results are mathematically rigorous. They are consistent with the empirical observation of Foudalis et al. [In Algorithms and Models for Web Graph (2011) Springer] that, “clustering correlates negatively with degree.” Moreover, they explain empirical results on $k^{-1}$ scaling of the local clustering coefficient of a vertex of degree $k$ reported in Ravasz and Barabási [Phys. Rev. E 67 (2003) 026112].

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Mindaugas Bloznelis. "Degree and clustering coefficient in sparse random intersection graphs." Ann. Appl. Probab. 23 (3) 1254 - 1289, June 2013. https://doi.org/10.1214/12-AAP874

Information

Published: June 2013
First available in Project Euclid: 7 March 2013

zbMATH: 1273.05197
MathSciNet: MR3076684
Digital Object Identifier: 10.1214/12-AAP874

Subjects:
Primary: 05C80 , 91D30
Secondary: 05C07

Keywords: Clustering coefficient , degree distribution , power law , random intersection graph

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.23 • No. 3 • June 2013
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