Interdependent Networks: Reducing the Coupling Strength Leads to a Change from a First to Second Order Percolation Transition

Roni Parshani, Sergey V. Buldyrev, and Shlomo Havlin
Phys. Rev. Lett. 105, 048701 – Published 21 July 2010

Abstract

We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on nodes of network B and a fraction of the nodes in network B depends on nodes of network A. Because of the coupling between the networks, when nodes in one network fail they cause dependent nodes in the other network to also fail. This invokes an iterative cascade of failures in both networks. When a critical fraction of nodes fail, the iterative process results in a percolation phase transition that completely fragments both networks. We show both analytically and numerically that reducing the coupling between the networks leads to a change from a first order percolation phase transition to a second order percolation transition at a critical point. The scaling of the percolation order parameter near the critical point is characterized by the critical exponent β=1.

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  • Received 19 March 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.048701

©2010 American Physical Society

Authors & Affiliations

Roni Parshani1, Sergey V. Buldyrev2,3, and Shlomo Havlin1

  • 1Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel
  • 2Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
  • 3Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA

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Issue

Vol. 105, Iss. 4 — 23 July 2010

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