strong_product#

strong_product(G, H)[source]#

Returns the strong product of G and H.

The strong 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 \(((u,x), (v,y))\) if any of the following conditions are met:

\(u=v\) and \((x,y)\) is an edge in \(H\)
\(x=y\) and \((u,v)\) is an edge in \(G\)
\((u,v)\) is an edge in \(G\) 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.strong_product(G, H)
>>> list(P)
[(0, 'a')]

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