Biased Percolation on Scale-free Networks

Details Biased Percolation on Scale-free Networks Biased Percolation on Scale-free Networks

2009-08-26

arxiv.org/abs/0908.3786v1

Phys. Rev. E 81, 011102 (2010)

Physics

Condensed Matter

Statistical Mechanics

17 pages, 8 figures

Scientific paper

10.1103/PhysRevE.81.011102

Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes $i$ and $j$ to be retained is proportional to $(k_ik_j)^{-\alpha}$ with $k_i$ and $k_j$ the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating functions method. The theory is found to agree quite well with simulations. By introducing an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well described by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous couplings.

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