Generalized network dismantling via a novel spectral partition algorithm

Network dismantling problem aims to find a node subset whose removal from a network results in the fragmentation of the network into subcritical connected components at the minimal overall cost. People have always been more interested in the unweighted case where each node has the same cost, while there are few results for the weighted case when nodes have different costs. It is a much more challenging problem in network science. In this paper, we present a novel strategy for this generalized network dismantling problem by characterizing the relationship between blocks and cut nodes. We firstly construct an auxiliary block-cut tree T from the original network G, where the nodes in the tree T have two types which correspond to either blocks or cut nodes of G, and edges of T only exist between two different type of nodes. Then we transform the problem of partitioning G by removing nodes to the problem of partitioning T by removing edges, both at a minimum overall cost. Finally partitioning T can be solved by a weighted spectral clustering algorithm. When we apply this new strategy on real-world networks, it performs equally or even better than the current state-of-the-art methods.