Detecting critical links in complex network to maintain information flow/reachability

We address the problem of efficiently detecting critical links in a large network. Critical links are such links that their deletion exerts substantial effects on the network performance. Here in this paper, we define the performance as being the average node reachability. This problem is computationally very expensive because the number of links is an order of magnitude larger even for a sparse network. We tackle this problem by using bottom-k sketch algorithm and further by employing two new acceleration techniques: marginal-link updating (MLU) and redundant-link skipping (RLS). We tested the effectiveness of the proposed method using two real-world large networks and two synthetic large networks and showed that the new method can compute the performance degradation by link removal about an order of magnitude faster than the baseline method in which bottom-k sketch algorithm is applied directly. Further, we confirmed that the measures easily composed by well known existing centralities, e.g. in/out-degree, betweenness, PageRank, authority/hub, are not able to detect critical links. Those links detected by these measures do not reduce the average reachability at all, i.e. not critical at all.