Clustering and percolation on superpositions of Bernoulli random graphs
A simple but powerful network model with n nodes and m partly overlapping layers is generated as an overlay of independent random graphs G1,...,Gm with variable sizes and densities. The model is parameterised by a joint distribution Pn of layer sizes and densities. When m grows linearly and Pn → P as n → ∞, 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.