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Phys. Rev. Lett. 109, 205703 (2012) [5 pages]

Core Percolation on Complex Networks

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Yang-Yu Liu1,2,*, Endre Csóka3, Haijun Zhou4, and Márton Pósfai1,5,6
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

Received 1 August 2012; published 14 November 2012

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.

© 2012 American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.109.205703
DOI:
10.1103/PhysRevLett.109.205703
PACS:
64.60.aq, 64.60.ah

*Corresponding author.

ya.liu@neu.edu

 
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