Adaptive Vertex Cover of Dynamical Networks With Prospect Theoretic Perspective

Abstract

Vertex covering a static network has received much attention in the past few years, while vertex covering a dynamical network has rarely been reviewed. In this article, we newly establish a vertex cover game model of dynamical networks with integrating prospect theory, and design an adaptive evolution scheme for network structure and vertices' strategies to achieve the adaptive covering of a dynamical network concurrently. We define a Nash equilibrium state of the network structure and vertices' strategies. Subsequently, we prove that given the reference point in the active region, the designed adaptive evolution scheme can drive the network structure and vertices' strategies to a Nash cover equilibrium (NCE) state with probability one. Intensive examples verify the effectiveness of the designed adaptive evolution scheme to the vertex covering of dynamical networks, presenting that in the NCE states, the less the average number of covered vertices, the less the average clustering coefficient and the ratio of the average degree of covered vertices to the average degree of uncovered vertices.