In the present chapter, an electrical network is considered as an interconnection of resistors. We demonstrate that random walks defined on connected undirected graphs have a profound connection to electric resistor networks (Doyle and Snell 1984; Tetali 1991; Chandra et al. 1996; Bollobas 1998). In the present chapter, we discuss the effective resistance of electrical networks, the relation between the shortest path (geodesic) distance and the effective resistance distance, Kirchhoff and Wiener indexes of a graph.