Random intersection graphs when m= w (n): an equivalence theorem relating the evolution of the G ( n, m, p ) and G ( n,P /italic>) models

By James Allen Fill, E. Scheinerman, Karen B. Singer-Cohen. 2000

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Random Graphs and Complex Networks (2016, methodology): “This model was introduced in: [230] and further studied in: [121] [162] [239] Willemien and I studied a version where the vertices have random weights and the edge probabilities are determined by these weights (which gives a graph where both the degree distribution and the clustering can be controll”
Epidemics on Random Graphs with Tunable Clustering (2007, methodology): “In fact, for α > 1, the random intersection graph is similar to the standard Erdős-Rényi random graph; see Fill et al. (2000). Moving on to the clustering in the graph, for two vertices v,w ∈ V, let Ivw denote the edge indicator for the edge between v and w in Gn,m,r, and write Pn for the probabilit”