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Percolation in directed scale-free networks

N. Schwartz, R. Cohen, D. ben-Avraham, A.-L. Barabási, and S. Havlin
Phys. Rev. E 66, 015104(R) – Published 26 July 2002
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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 pc1.

  • Received 1 May 2002

DOI:https://doi.org/10.1103/PhysRevE.66.015104

©2002 American Physical Society

Authors & Affiliations

N. Schwartz1, R. Cohen1, D. ben-Avraham2, A.-L. Barabási3, and S. Havlin1

  • 1Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, Israel
  • 2Department of Physics, Clarkson University, Potsdam, New York 13699-5820
  • 3Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556

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Issue

Vol. 66, Iss. 1 — July 2002

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