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tensor_product(G, H)[source]

Return 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:H (G,) – Networkx graphs.
Returns:P – 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.
Return type:NetworkX graph
Raises:NetworkXError – If G and H are not both directed or both undirected.


Node attributes in P are two-tuple of the G and H node attributes. Missing attributes are assigned None.


>>> G = nx.Graph()
>>> H = nx.Graph()
>>> G.add_node(0,a1=True)
>>> H.add_node('a',a2='Spam')
>>> P = nx.tensor_product(G,H)
>>> P.nodes()
[(0, 'a')]

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