simple_cycles(G)
A :None:None:`simple cycle`, or :None:None:`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.
This is a nonrecursive, iterator/generator version of Johnson's algorithm . There may be better algorithms for some cases .
The implementation follows pp. 79-80 in .
The time complexity is $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$ elementary circuits.
A directed graph
A generator that produces elementary cycles of the graph. Each cycle is represented by a list of nodes along the cycle.
Find simple cycles (elementary circuits) of a directed graph.
>>> 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()See :
... copyG.remove_nodes_from([1])
... copyG.remove_edges_from([(0, 1)])
... len(list(nx.simple_cycles(copyG))) 3
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.cycles.minimum_cycle_basis
networkx.algorithms.cycles.find_cycle
networkx.algorithms.cycles.recursive_simple_cycles
networkx.algorithms.cycles.cycle_basis
networkx.algorithms.cycles.simple_cycles
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