2019/12/31 by Mindaugas Bloznelis, Bloznelis, Mindaugas, Lasse Leskelä +1
Physics and Astronomy · Mathematics · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1912.13404
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.