Percolation in Directed Scale-Free Networks

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 p_c->1.

Latex, 5 pages, 2 figs

References in corpus (6)

• Statistical mechanics of complex networks
• Evolution of networks
• Epidemic dynamics and endemic states in complex networks
• Giant strongly connected component of directed networks
• Nonequilibrium Phase Transitions in Directed Small-World Networks
• Directed Percolation and Systems with Absorbing States: Impact of Boundaries

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