Finding All the Elementary Circuits of a Directed Graph

An algorithm is presented which finds all the elementary circuits-of a directed graph in time bounded by O((n + e)(c + 1)) and space bounded by O(n + e), where there are n vertices, e edges and c elementary circuits in the graph. The algorithm resembles algorithms by Tiernan and Tarjan, but is faster because it considers each edge at most twice between any one circuit and the next in the output sequence. 1. Introduction. Broadly speaking, there are two enumeration problems on sets of objects. The one, which we call counting, is determining how many objects there are in the set. The other, which we call finding, is the construction of every object in the set exactly once. Indeed, objects may always be counted by finding them if a method to do so is at hand. But knowing the count is usually of little aid in finding the objects.