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: 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