ABSTRACT
In this chapter we first discuss some aspects of electrical network analysis which depend heavily on the theory of graphs. We then use these results in the discovery of certain fundamental properties of networks (not necessarily electrical networks). In doing so we view a weighted graph as an electrical resistance network with conductances (reciprocals of resistance values) as weights of the edges. The main topics considered are topological formulas for network functions, random walks, Kirchhoff Index of a graph, Foster’s theorems, the arc-coloring lemma, and the no-gain property of resistance networks. Results to be presented make use of the theory developed in Chapter 8.
