Biased Percolation on Scale-free Networks

Abstract

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 $(k_i{k}_j{)}^{-\alpha }$ 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 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.

17 pages, 8 figures

References in corpus (10)

• Critical phenomena in complex networks
• Efficient Immunization Strategies for Computer Networks and Populations
• Percolation and Epidemic Thresholds in Clustered Networks
• Percolation on correlated networks
• Finite-size scaling in complex networks
• How to make a fragile network robust and vice versa
• Clustering in complex networks. II. Percolation properties
• Optimal Paths in Complex Networks with Correlated Weights: The World-wide Airport Network
• Routes to thermodynamic limit on scale-free networks
• Criticality on networks with topology-dependent interactions

Cited by in corpus (22)

• Mitigation of Malicious Attacks on Networks
• Cascade of failures in coupled network systems with multiple support-dependent relations
• Percolation on complex networks: Theory and application
• Hierarchical information clustering by means of topologically embedded graphs
• Scaling behavior of explosive percolation on the square lattice
• Bridgeness: A Local Index on Edge Significance in Maintaining Global Connectivity
• A Hamiltonian approach for explosive percolation
• Degree Correlation in Scale-Free Graphs
• Criterion for explosive percolation transitions on complex networks
• Percolation on bipartite scale-free networks
• Effect of degree correlations above the first shell on the percolation transition
• Phase transitions in the Potts model on complex networks
• The network asymmetry caused by the degree correlation and its effect on the bimodality in control
• Degree-ordered percolation on hierarchical scale-free network
• Degree heterogeneity in spatial networks with total cost constraint
• Degree-dependent network growth: From preferential attachment to explosive percolation
• Percolation on a maximally disassortative network
• Quantitative modeling of degree-degree correlation in complex networks
• Degree-penalized contact processes
• Optimal box-covering algorithm for fractal dimension of complex networks
• Heterogeneous nucleation on complex networks with mobile impurities
• Mandala Networks: ultra-robust, ultra-small-world and highly sparse graphs