The Annals of Applied Probability

Degree and clustering coefficient in sparse random intersection graphs

Mindaugas Bloznelis

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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].

Article information

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

Dates
First available in Project Euclid: 7 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1362684860

Digital Object Identifier
doi:10.1214/12-AAP874

Mathematical Reviews number (MathSciNet)
MR3076684

Zentralblatt MATH identifier
1273.05197

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

Keywords
Clustering coefficient power law degree distribution random intersection graph

Citation

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. https://projecteuclid.org/euclid.aoap/1362684860


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