networkx.algorithms.operators.product.cartesian_product

cartesian_product(G, H)

Returns 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, $V(P)=V(G) \times V(H)$. $P$ has an edge $((u,v),(x,y))$ if and only if either $u$ is equal to $x$ and both $v$ and $y$ are adjacent in $H$ or if $v$ is equal to $y$ and both $u$ and $x$ are adjacent in $G$.

Parameters

G, H (graphs) – 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)
>>> list(P)
[(0, 'a')]

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