Degree and clustering coefficient in sparse random intersection graphs
نویسنده
چکیده
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 (2001). For sparse graphs with 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. (2011) 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 (2003). key words: clustering coefficient, power law, degree distribution, random intersection graph 2000 Mathematics Subject Classifications: 05C80, 91D30, 05C07
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