tensor_product

tensor_product(G, H)

Returns the tensor product of G and H.

The tensor 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 \((u,x)\) is an edge in \(G\) and \((v,y)\) is an edge in \(H\).

Tensor product is sometimes also referred to as the categorical product, direct product, cardinal product or conjunction.

Parameters:

G, H: graphs

Networkx graphs.

Returns:

P: NetworkX graph

The tensor 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.tensor_product(G, H)
>>> list(P)
[(0, 'a')]

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