cartesian_product¶

cartesian_product(G, H)[source]¶

Return the Cartesian product of G and H.

The Cartesian product P of the graphs G and H has a node set that is the Cartesian product of the node sets, \(V(P)=V(G) imes V(H)\). P has an edge ((u,v),(x,y)) if and only if either u is equal to x and v & y are adjacent in H or if v is equal to y and u & x are adjacent in G.

Parameters:	H (G,) – 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.cartesian_product(G,H)
>>> P.nodes()
[(0, 'a')]

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