2005/08/25 by Luca Dall'Asta, Luca Dall’Asta · 7 citations
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Computer science #Continuum percolation theory #Directed percolation #Generalization #Graph #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Quantum mechanics #Random graph #Robustness (evolution) #Simple (philosophy) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Theoretical computer science #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2005/08/p08011
published in Journal of Statistical Mechanics Theory and Experiment 2005(08), P08011 (Institute of Physics) · 28 pages, 11 figures
openalex publication_date 2005/08/25 · arxiv created 2005/09/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct characterization of networks behaviour in relation with physical flows and spreading phenomena taking place on them. The functionality of real networks also depends on the ability of the nodes and the edges in bearing and handling loads of flows, energy, information and other physical quantities. We propose to study these properties introducing a process of inhomogeneous percolation, in which both the nodes and the edges spread out the flows with a given probability. Generating functions approach is exploited in order to get a generalization of the Molloy-Reed Criterion for inhomogeneous joint site bond percolation in correlated random graphs. A series of simple assumptions allows the analysis of more realistic situations, for which a number of new results are presented. In particular, for the site percolation with inhomogeneous edge transmission, we obtain the explicit expressions of the percolation threshold for many interesting cases, that are analyzed by means of simple examples and numerical simulations. Some possible applications are debated.