On the Moore-Penrose Pseudo Inverse of the Incidence Matrix for Weighted Undirected Graph

Abstract

Abstract The interaction of intelligent agents implies the existence of an environment to support it. The usual representations of this environment are graphs with certain properties. Throughput is one of the most important characteristics of such graphs. A traditional metric, such as the usual shortest paths, forms the basis of the traditional throughput index. In this case, a metric is used to synthesize the distribution of multi-coloured flows in graphs more complex than trees. To achieve better results than when using ordinary shortest paths, one can use the Euclidian metric. Working with weighted graphs requires a generalization of the explicit form of the Moore-Penrose pseudo inversed incidence matrix. The validity of the generalization is confirmed by verification of the Penrose conditions. An example of using the Euclidian metric for the distribution of computer network flows is given.