We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$ . The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$ through $p_{ij} \propto (k_i k_j)^{-\alpha}$ . By varying...

We study a decomposition process where all nodes with a targeted degree are removed from the network. Each removal step results in changes in the degrees of the remaining nodes, and other nodes may attain the targeted degree. The processes continue iteratively until no more nodes with the...