Function eulerian_circuit

networkx/algorithms/euler.py:159–236

Returns an iterator over the edges of an Eulerian circuit in `G`. An *Eulerian circuit* is a closed walk that includes each edge of a graph exactly once. Parameters ---------- G : NetworkX graph A graph, either directed or undirected. source : node, optional

(G, source=None, keys=False)

@nx._dispatchable
def eulerian_circuit(G, source=None, keys=False):
    """Returns an iterator over the edges of an Eulerian circuit in `G`.

    An *Eulerian circuit* is a closed walk that includes each edge of a
    graph exactly once.

    Parameters
    ----------
    G : NetworkX graph
       A graph, either directed or undirected.

    source : node, optional
       Starting node for circuit.

    keys : bool
       If False, edges generated by this function will be of the form
       ``(u, v)``. Otherwise, edges will be of the form ``(u, v, k)``.
       This option is ignored unless `G` is a multigraph.

    Returns
    -------
    edges : iterator
       An iterator over edges in the Eulerian circuit.

    Raises
    ------
    NetworkXError
       If the graph is not Eulerian.

    See Also
    --------
    is_eulerian

    Notes
    -----
    This is a linear time implementation of an algorithm adapted from [1]_.

    For general information about Euler tours, see [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] https://en.wikipedia.org/wiki/Eulerian_path

    Examples
    --------
    To get an Eulerian circuit in an undirected graph::

        >>> 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)]

    To get the sequence of vertices in an Eulerian circuit::