Percolation transition and distribution of connected components in generalized random network ensembles

Abstract

In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree sequences, non-trivial community structure or specific spatial dependence of the link probability for networks embedded in a metric space. We find the cluster distribution of the networks in these ensembles by mapping the problem to a fully connected Potts model with heterogeneous couplings. We show that the nature of the Potts model phase transition, linked to the birth of a giant component, has a crossover from second to first order when the number of critical colors $q_c=2$ in all the networks under study. These results shed light on the properties of dynamical processes defined on these network ensembles.

27 pages, 15 figures

References in corpus (19)

• Community structure in social and biological networks
• Error and attack tolerance of complex networks
• Resilience of the Internet to random breakdowns
• Critical phenomena in complex networks
• Breakdown of the Internet under intentional attack
• Class of correlated random networks with hidden variables
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• A General Formalism for Inhomogeneous Random Graphs
• The entropy of randomized network ensembles
• Mean field solution of the Ising model on a Barabasi-Albert network
• Solution of the 2-star model of a network
• Generalized percolation in random directed networks
• Percolation on correlated networks
• Evolution of scale-free random graphs: Potts model formulation
• On large deviation properties of Erdos-Renyi random graphs
• Finitely connected vector spin systems with random matrix interactions
• Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices
• Percolation and Loop Statistics in Complex Networks

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• Weighted projected networks: mapping hypergraphs to networks
• The distribution of the number of node neighbors in random hypergraphs
• Nonreciprocal random networks and their percolation properties