The Vertex-Edge Separator Transformation Problem in Network-Dismantling

Abstract

In complex networks, network-dismantling aims at finding an optimal set of nodes (or edges) such that the removal of the set from the network will lead to the disintegration of the network, that is, the size of the giant/largest connected component is not bigger than a specific threshold (for instance, $$1\%$$ of the original network size). Existing algorithms addressing this topic can be divided into two closely related but different categories: vertex separator-oriented algorithms and edge separator-oriented algorithms. There has been a lot of research on these two categories, respectively. However, to the best of our knowledge, less attention has been paid to the relation between the vertex separator and edge separator. In this paper, we studied the separator transformation (ST) problem between the separator of the vertexes and edges. We approximated the transformation from edge separator to vertex separator using Vertex Cover algorithm, while approximated the transformation from vertex separator to edge separator using an Explosive Percolation (EP) approach. Moreover, we further analyzed the results of the vertex-edge separator transformation through the explosive percolation method in detail. The transformation problem in network-dismantling opens up a new direction for understanding the role of the vital nodes set and edges set as well as the vulnerability of complex systems.