title: How to make a fragile network robust and vice versa.
abstract: 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 p_{ij} proportional, variant(k_{i}k_{j});{-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.
authors.affiliation: Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.
authors.forename: André A
authors.initials: AA
authors.lastname: Moreira
authors.forename: José S
authors.initials: JS
authors.lastname: Andrade
authors.forename: Hans J
authors.initials: HJ
authors.lastname: Herrmann
authors.forename: Joseph O
authors.initials: JO
authors.lastname: Indekeu