Generalized percolation in random directed networks

Abstract

We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

References in corpus (14)

• Statistical mechanics of complex networks
• Assortative mixing in networks
• Random graphs with arbitrary degree distributions and their applications
• Evolution of networks
• Mixing patterns in networks
• Network robustness and fragility: Percolation on random graphs
• How Popular is Your Paper? An Empirical Study of the Citation Distribution
• Epidemic spreading in correlated complex networks
• Patterns of link reciprocity in directed networks
• Giant strongly connected component of directed networks
• Resilience to damage of graphs with degree correlations
• Percolation in Directed Scale-Free Networks
• Anomalous percolating properties of growing networks
• Universal Properties of Growing Networks

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