Local Connectivity of Uncertain Random Graphs

As the system becomes more and more complex, we are usually in the state of indeterminacy. In the real world, the states of uncertainty and randomness are the two most common types of indeterminacy. An uncertain random graph is applied to describe a graph model with uncertainty and randomness simultaneously. This paper mainly focuses on the connectivity of two vertices in an uncertain random graph. Firstly, a local connectivity index is proposed to unveil the chance measure that two special vertices are connected in an uncertain random graph. Furthermore, a method for calculating the local connectivity index is formulated. In addition, some simplified forms of the method are developed, and an algorithm is designed to obtain the local connectivity index. Finally, the information relevant to the relationship between the local connectivity index and the connectivity index is discussed.