Computer program for finding all possible cycles in graphs

A new approach is presented for identifying all possible cycles in graphs. Input data are the total numbers of vertices and edges, as well as the vertex adjacencies using arbitrary vertex numbering. A homeomorphically reduced graph (HRG) is constructed by ignoring vertices of degree less than three. The algorithm is based on successive generation of possible edge-combinations in the HRG. If a combination yields a cycle, it is either printed or stored and then finally printed in a list of all possible cycles arranged in the order of increasing ring size. A unique numbering of the cycle is used. The computer program is listed and exemplified. Computing times are given.