Abstract: By applying the direted hypergraph theory,the concepts of the decomposition and contraction of a hyperedge are introduced.Chen's essential complementary partition(ECP)method for solving the cascade problem of two passive networks is improved to form a more efficient decomposition-contraction pair(DCP)method,then it is developed to form the directed(positive-rooted)decomposition-contraction pair(PDCP)method,to solve the cascade problem of two active networks.Furthermore,it is developed to form the general decomposition-contraction(GDC)method,to solve the problem of finding symbolic network functions for the interconnection of several active networks.