In: Transactions of the Institute of Electronics, Information and Communication Engineers A, Vol. J72A, No. 10, pages 1621-1632. October 1989. In Japanese.
Abstract: In terms of flows in networks with positive gains, the authors characterize P-invariants of marked graphs with edge-weights and propose an algorithm for obtaining a P-basis. From a marked graph, the authors construct a network with positive edge-gains such that every elementary P-invariant corresponds to an elementary flow and vice versa. First the authors give a necessary and sufficient condition for a flow to be elementary, and then propose an algorithm for finding a flow basis of such a network.
Keywords: P-invariant; P-Basis; marked graphs; edge-weight; elementary flow.