An efficient search algorithm to find the elementary circuits of a graph

to A theoretically most efficient search algorithm is presented which uses an exhaustive search to find all of the elementary circuits of a graph. The algorithm can be easily modified to find all of the elementary circuits with a particular attribute such as length. A rigorous proof of the algorithm is given as well as an example of its application. Empirical bounds are presented re-lating the speed of lhe algorithm to the number of vertices and the number of arcs. The speed is also related to the number of circuits inthe graph to give a relation between speed and com-plexity. Extensions to undirected and s-graphs are discussed. KEY WORDS AND PHRASES: algorithm, graph theory, circuit search algo-rlthm, path search algorithm, searchin