is_eulerian#

is_eulerian(G)[source]#

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:

GNetworkX 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