Percolation in Directed Scale-Free Networks

TL;DR

This paper investigates the percolation properties of directed scale-free networks with correlated degrees, revealing three regimes with distinct critical behaviors and resilience characteristics.

Contribution

It analytically derives a phase diagram for directed scale-free networks, identifying three regimes with different percolation exponents and resilience to random failures.

Findings

Identifies three percolation regimes based on degree exponents.

Derives analytical expressions for anomalous exponents.

Shows resilience of the third regime to random dilution.

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.