This paper is divided into three parts The first part shows how linear graphs are used in analysis of electrical networks. The proof for the topological formulas of transfer functions of passive networks without mutual couplings given here is the first formal and precise proof in this field. By the use of topological formulas, such a passive network can be analyzed by a digital computer. The second part discusses the applica tion of linear graphs to switching networks by starting with exploration of the properties of paths in a linear graph. Then the necessity of realizing a cut set matrix or circuit matrix is discussed. The third part discusses a rather new field which is many-ports flow problems which is called the theory of communication nets.