Network robustness and random processes

We introduce two new measures of network robustness and apply them to four different strategies. The measures are independent from the number of nodes in the network and have the strong potential to cover a large portfolio of applications. Using the Monte-Carlo methods, we demonstrate how to approximate the measures. The methods are based on random interruption of links with suitable constraints which represent the above-mentioned strategies. We introduce two networks with obvious varying robustness to demonstrate the measures. We also demonstrate how to employ the measures in order to improve the robustness of the networks by adding one new link. We further indicate that the measures are able to identify the infrequently connected parts of the network and suggest the most appropriate improvement. We also discuss the consequences of the obtained results and the possible applications of the measures.