Find simple cycles (elementary circuits) of a directed graph.
simple cycle, or
elementary circuit, is a closed path where no node appears twice. Two elementary circuits are distinct if they are not cyclic permutations of each other.
G (NetworkX DiGraph) – A directed graph
cycle_generator – A generator that produces elementary cycles of the graph. Each cycle is represented by a list of nodes along the cycle.
- Return type
>>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)] >>> G = nx.DiGraph(edges) >>> len(list(nx.simple_cycles(G))) 5
To filter the cycles so that they don’t include certain nodes or edges, copy your graph and eliminate those nodes or edges before calling
>>> copyG = G.copy() >>> copyG.remove_nodes_from() >>> copyG.remove_edges_from([(0, 1)]) >>> len(list(nx.simple_cycles(copyG))) 3
The implementation follows pp. 79-80 in 1.
The time complexity is \(O((n+e)(c+1))\) for \(n\) nodes, \(e\) edges and \(c\) elementary circuits.
Finding all the elementary circuits of a directed graph. D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975. https://doi.org/10.1137/0204007
Enumerating the cycles of a digraph: a new preprocessing strategy. G. Loizou and P. Thanish, Information Sciences, v. 27, 163-182, 1982.
A search strategy for the elementary cycles of a directed graph. J.L. Szwarcfiter and P.E. Lauer, BIT NUMERICAL MATHEMATICS, v. 16, no. 2, 192-204, 1976.