Circuit, cutset and path enumeration, and other applications of edge-numbering convention

New methods employing an edge-numbering convention are proposed for listing all circuits and cutsets of an arbitrary graph, which are an improvement over the ones recently given by Maxwell and Reed. Storage of a master path matrix, whereby the all-path matrix between any two nodes of a given graph can be derived by simple modification, is discussed. A technique for generation of all trees, including a given set of edges and some significant properties of master path matrices, are also discussed. The algorithms proposed are all suitable for computer adoption.