Principles and Applications of Unistor Graphs

摘要

New properties and applications of unistor graphs are presented. A technique for solving a set of linear equations is derived and an alternative graphical representation of an active network is given. Communication nets are treated for the first time by unistor graph techniques. A unistor is an oriented edge connecting two vertices in a graph. A flow exists in the oriented edge with a value equal to the product of the edge weight and the weight of the initial vertex. The unistor is characterized by flow, potential, admittance, and directedness-four properties also found in linear equations and electrical networks. It is shown that a unistor graph can represent a matrix and the determinant and cofactors can be evaluated by using directed trees and directed 2-trees. A technique is given for representing in a node-admittance form an active network by a unistor graph. This graph is then used to determine the values of the unknown voltages of the original circuit. A vertex potential for a communication net is defined and used to obtain upper and lower bounds on the maximum flow between two vertices of the net. (Author)