Numerical applications: Cycle algorithms for undirected linear graphs and some immediate applications

• Authors: J. T. Welch, Jr.
• Venue: ACM '65 Proceedings of the 1965 20th national conference
• Year: 1965

THE ANALYSIS OF GRAPHICALLY presented data, such as the structural diagram of a chemical compound, or a model of information flow in a system design, is becoming increasingly important as technology advances. In the interests of accuracy and lower costs, it is often desirable to mechanize the analysis completely. Here we shall present a mechanical procedure which finds all cycles (i.e., simple elementary cycles1) of a finite undirected linear graph, given an array called the incidence matrix of the graph. The procedure consists of three algorithms: algorithm 1, which determines a basic set of cycles from which all others can be generated; algorithm 2, which assigns an ordering to the basic cycles; and algorithm 3, which generates all remaining cycles. An immediate application of algorithm 1 will be illustrated, and the same will be done for algorithm 3. The examples used must necessarily be simplified. This should not obscure the objective, which is to suggest algorithms of sufficient generality for computer, or at least mechanical, application. A more complete treatment of the algorithms themselves, with necessary proofs, will follow in a later paper5.