Directed Network Dismantling Method Based On Non-backtracking Matrix

With the development of technology,humanity is already in a highly networked world,which brings many conveniences but also causes more serious hazards,for example,the nowadays widespread spread of the new crown epidemic has dealt a heavy blow to all countries of the world and disinformation is also spreading more rapidly in social media.However,these negative effects of networks can be controlled by removing a critical set of nodes from the network and blocking connections in the network.Moreover,to break a network into several unconnected subcomponents by removing a minimal set of vertices is network dismantling problem.As one of the most fundamental network structural problems in network science,network dismantling can be effective in controlling the dynamical behaviour and preserving the robustness of the network.However,the vast majority of existing work focuses only on network dismantling in directed networks undirected networks,and very little research has been done on network dismantling in directed networks,and the already existing methods are sometimes not applicable to the directed network dismantling.Concentrating on network dismantling in directed network,this paper proposes the link modules dismantling method based on non-backtracking matrix,which combines link modules spectral partition and network dismantling in directed network.We construct the minimum objective dismantling function using non-backtracking matrix as operators with its excellent properties and partition the link module by solving for the approximate second eigenvector of the function matrix,finally find and remove the minimal critical vertices set which connects different link modules to finish dismantling.In order to verify the effectiveness of this method,it has been applied in large-scale generative networks and real networks.Multiple experimental results show that the proposed method not only has great advantages in terms of dismantling accuracy and computational efficiency,but also serves to protect the network structure information.