Function is_eulerian

networkx/algorithms/euler.py:22–70

Returns True if and only if `G` is Eulerian. A graph is *Eulerian* if it has an Eulerian circuit. An *Eulerian circuit* is a closed walk that includes each edge of a graph exactly once. Graphs with isolated vertices (i.e. vertices with zero degree) are not considered to have Eu

(G)

@nx._dispatchable
def is_eulerian(G):
    """Returns True if and only if `G` is Eulerian.

    A graph is *Eulerian* if it has an Eulerian circuit. An *Eulerian
    circuit* is a closed walk that includes each edge of a graph exactly
    once.

    Graphs with isolated vertices (i.e. vertices with zero degree) are not
    considered to have Eulerian circuits. Therefore, if the graph is not
    connected (or not strongly connected, for directed graphs), this function
    returns False.

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

    Examples
    --------
    >>> nx.is_eulerian(nx.DiGraph({0: [3], 1: [2], 2: [3], 3: [0, 1]}))
    True
    >>> nx.is_eulerian(nx.complete_graph(5))
    True
    >>> nx.is_eulerian(nx.petersen_graph())
    False

    If you prefer to allow graphs with isolated vertices to have Eulerian circuits,
    you can first remove such vertices and then call `is_eulerian` as below example shows.

    >>> G = nx.Graph([(0, 1), (1, 2), (0, 2)])
    >>> G.add_node(3)
    >>> nx.is_eulerian(G)
    False

    >>> G.remove_nodes_from(list(nx.isolates(G)))
    >>> nx.is_eulerian(G)
    True


    """
    if G.is_directed():
        # Every node must have equal in degree and out degree and the
        # graph must be strongly connected
        return all(
            G.in_degree(n) == G.out_degree(n) for n in G
        ) and nx.is_strongly_connected(G)
    # An undirected Eulerian graph has no vertices of odd degree and
    # must be connected.
    return all(d % 2 == 0 for v, d in G.degree()) and nx.is_connected(G)


@nx._dispatchable