Connectivity of Networks Modeled by Weighted Graphs

A graph G=(V,E) together with two positive real-valued weight-functions wV:V→R>0 and wE:E→R>0 is called a weighted graph and is denoted by (G;wV;wE). In this paper, we introduce the concepts of connectivity, edge-connectivity, and restricted edge-connectivity for a weighted graph (G;wV;wE), and we prove general bounds analogous to those in the unweighted case. Furthermore, we study the connectivity and edge-connectivity of the line graph and the P2-path graph of a weighted graph, establishing upper and lower bounds for each of these parameters.