networkx.algorithms.operators.product.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, $V(P)=V(G) \times V(H)$ . $P$ 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 $H$ .

Parameters: G, H (graphs) – Networkx graphs.
Returns: P – 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.
Return type: NetworkX graph
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