Network Robustness Based on Inverse Percolation

The macroscopic behavior of networks, when facing random removal of nodes or edges, can be described as an inverse percolation process in a random graph. To determine whether a network remains operational when its elements (nodes or edges) fail at random, a "network robustness" criterion is used as a probabilistic measure. In this paper, we used percolation theory to assess this criterion for a network subjected to random failures of its elements. We then mapped the random failures process of the network into an inverse percolation problem. After that, based on the threshold for which the connectivity disappears, we assessed network robustness. Also, to demonstrate our method, we studied the robustness of systems that can be modeled as general inhomogeneous random graphs as well as scale-free random graphs.