Abstract
A communication net consists of branches representing communication channels with the weight of each being a positive real number which represents the capacity of transferring information through the (called a branch capacity). The terminal capacity between the vertices i and j of a communication net is the capacity of transferring information between the vertices i and j by considering the net as a whole. To indicate the terminal capacities between all possible pairs of vertices in a net, a terminal capacity matrix is defined. Then the necessary and sufficient conditions for a terminal capacity matrix are given. To represent the structure of a communication net, a capacity matrix is defined. Then the synthesis of a communication net from a given terminal capacity matrix is to obtain a capacity matrix from the given terminal capacity matrix.
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