CSR: A Centrality Based on Robustness and Controllable Subspace of Complex Networks

Complex networks are everywhere, some of them are airline network, road network, power grid network and protein-to-protein network. These networks are robust in failure or under attack but still needs in-depth study. Researchers have proposed various techniques to find and enhance the robustness of networks. However, furthers study required in this area. In this paper, we study the robustness of controllable subspace under random removal of edges and propose the robustness index for controllable subspace from one node as well as from a set of nodes. This work proposes a new centrality CSR (Controllable Subspace and robustness) to rank the important nodes of network based on optimal values of controllable subspace and robustness of controllable subspace. We also discuss the effects of exact robustness index and approximate robustness index on two factor: computational time, and accuracy. We show the analysis of top ten percent important nodes of various real networks with different centrality measures and CSR to compare the results. With the extensive experimentation on the real networks, CSR outperformed other centrality measures.