Algorithms for finding a fundamental set of cycles for an undirected linear graph

Abstract

Given the adjacency matrix of the graph, the algorithm presented in this paper finds a spanning tree and then constructs the set of fundamental cycles. Our algorithm is slower than an algorithm presented by Welch by a ratio of N/3 (N is the number of nodes) but requires less storage. For graphs with a large number of nodes and edges, when storage is limited our algorithm is superior to Welchs; however, when the graphs are small, or machine storage is very large, Welchs algorithm is superior. Timing estimates and storage requirements for both methods are presented. © 1967, ACM. All right reserved.