Synthesis of Radio-Communication Nets

A radio-communication net is a communication network in which links between stations have unlimited capacity to transmit information. Such a network can be represented by a graph with weights on the vertices which correspond to the capacities of individual stations. The capacity of a radio-communication net of n stations is described by a matrix of order n called a terminal-capacity matrix. A necessary and sufficient condition for a matrix to be realizable as the terminal-capacity matrix of a radio-communication net is found. A simple algorithm for synthesizing a radio-communication net of a given terminal-capacity matrix, which is proved to have minimum sum of vertex capacities and minimum number of branches, is obtained. A theorem concerning all possible structures of a radio-communication net with the same terminal-capacity matrix is established.