On weak completeness and weak non-degeneracy of networks

The graph-theoretic properties depending on the element types and their controllability but not on the particular form of constitutive relations of elements are considered. New concepts such as normal partition pair of the branch set, weak completeness and weak non-degeneracy are introduced and their properties are investigated in detail. These properties may then be used to formulate purely topological methods of analysing some dynamical aspects of nonlinear RLC networks.