Biased percolation on scale-free networks

Hans Hooyberghs, Bert Van Schaeybroeck, André A. Moreira, José S. Andrade, Hans J. Herrmann, Joseph O. Indekeu
2010 Physical Review E  
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)^-α with k_i and k_j the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their
more » ... stigate 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→ 1 limit of the q-state Potts model with inhomogeneous couplings.
doi:10.1103/physreve.81.011102 pmid:20365318 fatcat:i63hy3fpqzendie25fsci4xqze