Analytics solution for the robustness of incomplete information scale-free networks

We study the robustness of scale-free networks where degree information is incomplete. For this purpose, we propose a node attack strategy where nodes whose degree is higher than a threshold k0 are removed with certainty, while for other nodes, the removal probability is a stochastic function of its (unknown) degree k. We developed an analytic solution for this node attack strategy based on generating functions method, and compared to Monte-Carlo simulation. Our results show a good agreement between analytic and numerical solutions. In addition, we compare the robustness of scale-free networks under the new node attack strategy with other nodes’ degree attack strategies where nodes’ degree information is known. We found that when degree information is incomplete, the scale-free complex networks become more robust against attack, which is expected. Our work can be useful for the case of real-world networks where only partial degree information is available.