Clustering and percolation on superpositions of Bernoulli random graphs
Mindaugas Bloznelis, Lasse Leskelä
Abstract
Abstract A simple but powerful network model with nodes and partly overlapping layers is generated as an overlay of independent random graphs with variable sizes and densities. The model is parameterized by a joint distribution of layer sizes and densities. When grows linearly and as , the model generates sparse random graphs with a rich statistical structure, admitting a nonvanishing clustering coefficient together with a limiting degree distribution and clustering spectrum with tunable power‐law exponents. Remarkably, the model admits parameter regimes in which bond percolation exhibits two phase transitions: the first related to the emergence of a giant connected component, and the second to the appearance of gigantic single‐layer components.