Generalized graph decomposition and its applications

A graph-classification concept is introduced, which extends the notion of dense, medium, and sparse graphs and makes the classification a function of a preassigned real nonnegative number. Important properties of various classes of graphs are discussed. An algorithm for the harmonious decomposition of a graph is proposed that yields a minimum basic set of the graph and determines the available range of the real nonnegative number. Harmonious decomposition is considered in connection with the hybrid method of network analysis.<>