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.
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
Permanent URL
Recommended Citation
Schwartz, N.; Cohen, R.; ben-Avraham, D.; Barabási, A.-L.; and Havlin, S., "Percolation in directed scale-free networks" (2002). Physics Faculty Publications. Paper 112. http://hdl.handle.net/2047/d20000685
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Notes
Originally published in Physical Review E 66(1), 2002. doi:10.1103/PhysRevE.66.015104