Construction of simple path graphs in transport networks: I. general solutions and examples

Abstract

The calculation of the set of all simple paths connecting two vertices of an undirected graph is considered. The more general problems of connecting vertices which belong to disjoint sets of vertices in a graph by all simple paths are also investigated. The connection between these problems and finding vertex biconnected components and graph bridges is established, and based on this their complete solutions are given. Simplifying techniques for the calculation of the sets of paths based on the addition of auxiliary edges and vertices to the analyzed graph are proposed. Examples of the application of the developed apparatus to problems of the real-time management of transport networks are given