The structure of networks realized from terminal capacity matrices

We consider the structure of a flow network realized from a given terminal capacity matrix. As a result, we show a necessary and sufficient condition that a terminal capacity matrix is possible of realizing any graph. And in the case that the correspondence relation of vertices in a graph G and columns of an elementary terminal capacity matrix T_E are given, we show a sufficient condition and a necessary condition for the structure of the fundamental graph, for which is possible to realize T_E