How to Make a Fragile Network Robust and Vice Versa

We investigate topologically biased failure in scale-free networks with degree distribution P(k) ∝ k^−γ . 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 ∝ (k_i k_j)^−α . By varying the exponent α, we interpolate between random (α = 0) and systematic failure. For α > 0 ( < 0) the most (least) connected nodes are depreciated first. This topological biasintroduces 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 γ and on α. As a consequence, network robustness or fragility can be controlled through fine tuning of the topological bias in the failure process