Proper flow paths in vertex-weighted communication nets

In a communication net in which the maximum attainable flows are determined by the vertex capacities, there is, in general, a high degree of redundancy among the paths available for flow assignments in the net. A technique is given by which the set of all nonredundant paths, called proper flow paths, is uniquely determined. The method employs a direct and simple means of eliminating the redundancies in a pathfinding routine proposed previously by Paz, involving symbolic noncommutative multiplications among the entries of a modified vertex-adjacency matrix. A useful byproduct ensues with the immediate identification of vertexes which are not in any vertex cut set. This simplifies the problem of identifying all vertex cut sets in the net. A presentation of proper-flow-path theory in communication nets is included in the paper.