recursive_simple_cycles#

recursive_simple_cycles(G)[source]#

Find simple cycles (elementary circuits) of a directed graph.

A 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.

This version uses a recursive algorithm to build a list of cycles. You should probably use the iterator version called simple_cycles(). Warning: This recursive version uses lots of RAM! It appears in NetworkX for pedagogical value.

Parameters:
GNetworkX DiGraph

A directed graph

Returns:
A list of cycles, where each cycle is represented by a list of nodes
along the cycle.
Example:
>>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]
..

>>> G = nx.DiGraph(edges)
..

>>> nx.recursive_simple_cycles(G)
..

[[0], [2], [0, 1, 2], [0, 2], [1, 2]]

Notes

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.

References

[1]

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