Abstract
Biased (degree-dependent) 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 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(i)k(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 presenting 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.
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