Biased percolation on scalefree networks
Abstract
Biased (degreedependent) percolation was recently shown to provide strategies for turning robust networks fragile and vice versa. Here, we present more detailed results for biased edge percolation on scalefree networks. We assume a network in which the probability for an edge between nodes i and j to be retained is proportional to (k_{i}k_{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 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 generatingfunctions method. The theory is found to agree quite well with simulations. By presenting an extension of the FortuinKasteleyn construction, we find that biased percolation is welldescribed by the q→1 limit of the q state Potts model with inhomogeneous couplings.
 Publication:

Physical Review E
 Pub Date:
 January 2010
 DOI:
 10.1103/PhysRevE.81.011102
 arXiv:
 arXiv:0908.3786
 Bibcode:
 2010PhRvE..81a1102H
 Keywords:

 64.60.ah;
 89.75.Hc;
 Percolation;
 Networks and genealogical trees;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 17 pages, 8 figures