Connectedness strength of two vertices in an uncertain graph

Abstract

In practical applications of graph theory, due to some reasons, different types of uncertainties are frequently encountered. In this paper, we employ uncertainty theory to investigate an uncertain graph in which complete determination of whether two vertices are joined by an edge or not cannot be carried out. By means of uncertainty theory, the concepts of connectedness strength of two vertices in an uncertain graph and strength of an uncertain path are proposed. A method to calculate the connectedness strength of two vertices is also described. After that, we investigate the relationship between the connectedness strength of two vertices and the connectedness index of the uncertain graph. This relationship provides a new method to obtain the connectedness index of an uncertain graph.