Connectivity of Networks Modeled by Weighted Graphs

A graph G=(V,E) together with a positive real-valued weight-function w:V→R+ or w:E→R+ is called a weighted graph and is denoted by (G;w). In this paper, we introduce the concepts of connectivity, edge-connectivity, and restricted edge-connectivity for a weighted graph (G;w), 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.