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, \(V(P)=V(G) \times V(H)\). \(P\) 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 \(H\).

G, H: graphs

Networkx graphs.

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.


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


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


>>> 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