Clustering coefficient of random intersection graphs with infinite degree variance

Degree and clustering coefficient in sparse random intersection graphs

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...

Random intersection graphs with tunable degree distribution and clustering

A random intersection graph is constructed by independently assigning each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in which each vertex is given a random weight, and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a gi...

Generating Random Graphs with Tunable Clustering Coefficient

Degree Distributions in General Random Intersection Graphs

Random intersection graphs, denoted by G(n,m, p), are introduced in [9, 14] as opposed to classical Erdős-Rényi random graphs. Let us consider a set V with n vertices and another universal set W with m elements. Define a bipartite graph B(n,m, p) with independent vertex sets V and W . Edges between v ∈ V and w ∈ W exist independently with probability p. The random intersection graph G(n,m, p) d...

Clustering Coefficients of Random Intersection Graphs

Two general random intersection graph models (active and passive) were introduced by Godehardt and Jaworski (Exploratory Data Analysis in Empirical Research, Springer, Berlin, Heidelberg, New York, pp. 68–81, 2002). Recently the models have been shown to have wide real life applications. The two most important ones are: non-metric data analysis and real life network analysis. Within both contex...