Core Percolation on Complex Networks

Yang-Yu Liu, Endre Csóka, Haijun Zhou, and Márton Pósfai

Phys. Rev. Lett. 109, 205703 – Published 14 November 2012

Abstract

We analytically solve the core percolation problem for complex networks with arbitrary degree distributions. We find that purely scale-free networks have no core for any degree exponents. We show that for undirected networks if core percolation occurs then it is continuous while for directed networks it is discontinuous (and hybrid) if the in- and out-degree distributions differ. We also find that core percolations on undirected and directed networks have completely different critical exponents associated with their critical singularities.

Received 1 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.205703

Authors & Affiliations

Yang-Yu Liu^1,2,*, Endre Csóka³, Haijun Zhou⁴, and Márton Pósfai^1,5,6

¹Center for Complex Network Research and Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
²Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA
³Eötvös Loránd University, H-1053 Budapest, Hungary
⁴State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁵Department of Theoretical Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
⁶Department of Physics of Complex Systems, Eötvös Loránd University, H-1053 Budapest, Hungary

^*Corresponding author. ya.liu@neu.edu

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Vol. 109, Iss. 20 — 16 November 2012

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