lexicographic_product#

lexicographic_product(G, H)[source]#

Returns the lexicographic product of G and H.

The lexicographical product P of the graphs G and H has a node set that is the Cartesian product of the node sets, V(P)=V(G)×V(H). P has an edge ((u,v),(x,y)) if and only if (u,v) is an edge in G or u==v and (x,y) is an edge in H.

Parameters:
G, H: graphs

Networkx graphs.

Returns:
P: NetworkX graph

The Cartesian product of G and H. P will be a multi-graph if either G or H is a multi-graph. Will be a directed if G and H are directed, and undirected if G and H are undirected.

Raises:
NetworkXError

If G and H are not both directed or both undirected.

Notes

Node attributes in P are two-tuple of the G and H node attributes. Missing attributes are assigned None.

Examples

>>> G = nx.Graph()
>>> H = nx.Graph()
>>> G.add_node(0, a1=True)
>>> H.add_node("a", a2="Spam")
>>> P = nx.lexicographic_product(G, H)
>>> list(P)
[(0, 'a')]

Edge attributes and edge keys (for multigraphs) are also copied to the new product graph