We introduce a rapid deterministic algorithm for identification of the most critical links which are capable of causing network disruptions. The algorithm is based on searching for the shortest cycles in the network and provides a significant time improvement compared with a common brute-force algorithm which scans the entire network. We used a simple measure, based on standard deviation, as a vulnerability measure. It takes into account the importance of nodes in particular network components. We demonstrate this approach on a real network with 734 nodes and 990 links. We found the worst scenarios for the cases with and without people living in the nodes. The evaluation of all network breakups can provide transportation planners and administrators with plenty of data for further statistical analyses. The presented approach provides an alternative approach to the recent research assessing the impacts of simultaneous interruptions of multiple links.