Abstract

Many complex networks in nature have directed links, a property that affects the network’s navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in and out degree distributions. We derive a phase diagram that indicates the existence of three regimes, determined by the values of the degree exponents. In the first regime we regain the known directed percolation mean field exponents. In contrast, the second and third regimes are characterized by anomalous exponents, which we calculate analytically. In the third regime the network is resilient to random dilution, i.e., the percolation threshold is pc→1.

Notes

Originally published in Physical Review E 66(1), 2002. doi:10.1103/PhysRevE.66.015104

Keywords

scale-free networks, directed links, navigability

Subject Categories

Percolation (Statistical physics), Topology

Disciplines

Physics

Publisher

The American Physical Society

Publication Date

7-2002

Rights Holder

©2002 The American Physical Society

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Included in

Physics Commons

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