Abstract
Classes of networks with fixed node degrees and weights (capacities) of arcs and loops not exceeding a given parameter are studied. Characteristic functions are found that depend on vector components and a parameter; the nonnegativeness of this parameter is the network existence criterion, the degrees of its nodes are equal to vector components, and the arc weights do not exceed the parameter. The set of nodes of such networks are decomposed into two subsets. The sums of arc weights on each subset and the sum of arc weights incident upon the nodes of both subsets are considered as variables. Formulas for the upper and lower bounds for these variables are obtained. The results can be used for the calculation of flows in networks because since node partitioning determines the network cut.
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