2008/12/18 by André A. Moreira, Andre A. Moreira, José S. Andrade +3 · 2 citations
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Complex network #Degree (music) #Degree distribution #Discrete mathematics #Exponent #Fragility #Graph theory and applications #Mathematics #Opinion Dynamics and Social Influence #Physics #Scale-free network #Statistical physics #Thermodynamics #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.102.018701
Accepted for publication at Phys. Rev. Lett
arxiv created 2008/12/18 · openalex publication_date 2009/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate topologically biased failure in scale-free networks with a degree distribution P(k) proportional, variantk;-gamma. The probability p that an edge remains intact is assumed to depend on the degree k of adjacent nodes i and j through pij proportional, variant(kikj);-alpha. By varying the exponent alpha, we interpolate between random (alpha=0) and systematic failure. For alpha>0 (<0) the most (least) connected nodes are depreciated first. This topological bias introduces a characteristic scale in P(k) of the depreciated network, marking a crossover between two distinct power laws. The critical percolation threshold, at which global connectivity is lost, depends both on gamma and on alpha. As a consequence, network robustness or fragility can be controlled through fine-tuning of the topological bias in the failure process.