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This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

networkx.algorithms.operators.product.lexicographic_product

lexicographic_product(G, H)

Returns the lexicographic product of G and H.

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

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.lexicographic_product(G, H)
>>> list(P)
[(0, 'a')]

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