eulerian_circuit

eulerian_circuit(G, source=None)[source]

Return the edges of an Eulerian circuit in G.

An Eulerian circuit is a path that crosses every edge in G exactly once and finishes at the starting node.

Parameters:
  • G (NetworkX Graph or DiGraph) – A directed or undirected graph
  • source (node, optional) – Starting node for circuit.
Returns:

edges – A generator that produces edges in the Eulerian circuit.

Return type:

generator

Raises:

NetworkXError – If the graph is not Eulerian.

See also

is_eulerian()

Notes

Linear time algorithm, adapted from [1]. General information about Euler tours [2].

References

[1]J. Edmonds, E. L. Johnson. Matching, Euler tours and the Chinese postman. Mathematical programming, Volume 5, Issue 1 (1973), 111-114.
[2]http://en.wikipedia.org/wiki/Eulerian_path

Examples

>>> G=nx.complete_graph(3)
>>> list(nx.eulerian_circuit(G))
[(0, 2), (2, 1), (1, 0)]
>>> list(nx.eulerian_circuit(G,source=1))
[(1, 2), (2, 0), (0, 1)]
>>> [u for u,v in nx.eulerian_circuit(G)]  # nodes in circuit
[0, 2, 1]