Terminal and Branch Capacity Matrices of a Communication Net

A communication net consists of branches representing communication channels with the weight of each branch being a positive real number which represents the capacity of transferring information through the branch (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 branch capacity matrix is defined. Then the synthesis of a communication net from a given terminal capacity matrix is to obtain a branch capacity matrix from the given terminal capacity matrix.