The Annals of Applied Probability

Degree and clustering coefficient in sparse random intersection graphs

Mindaugas Bloznelis

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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].

Article information

Ann. Appl. Probab., Volume 23, Number 3 (2013), 1254-1289.

First available in Project Euclid: 7 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20] 91D30: Social networks
Secondary: 05C07: Vertex degrees [See also 05E30]

Clustering coefficient power law degree distribution random intersection graph


Bloznelis, Mindaugas. Degree and clustering coefficient in sparse random intersection graphs. Ann. Appl. Probab. 23 (2013), no. 3, 1254--1289. doi:10.1214/12-AAP874.

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