Inhomogeneous percolation models for spreading phenomena in random graphs

Abstract

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.

28 pages, 11 figures

References in corpus (11)

• The structure and function of complex networks
• The architecture of complex weighted networks
• Mixing patterns in networks
• Cascade-based attacks on complex networks
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Stability and topology of scale-free networks under attack and defense strategies
• Resilience to damage of graphs with degree correlations
• Epidemic spreading in complex networks with degree correlations
• Edge overload breakdown in evolving networks
• Epidemics, disorder, and percolation
• Disease Spreading in Structured Scale-Free Networks

Cited by in corpus (4)

• Containing epidemic outbreaks by message-passing techniques
• Biased Percolation on Scale-free Networks
• Different thresholds of bond percolation in scale-free networks with identical degree sequence
• Vaccination with partial transmission and social distancing on contact networks