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Returns the complete multipartite graph with the specified subset sizes.

Parameters:subset_sizes (tuple of integers or tuple of node iterables) – The arguments can either all be integer number of nodes or they can all be iterables of nodes. If integers, they represent the number of vertices in each subset of the multipartite graph. If iterables, each is used to create the nodes for that subset. The length of subset_sizes is the number of subsets.
Returns:G – Returns the complete multipartite graph with the specified subsets.

For each node, the node attribute ‘subset’ is an integer indicating which subset contains the node.

Return type:NetworkX Graph


Creating a complete tripartite graph, with subsets of one, two, and three vertices, respectively.

>>> import networkx as nx
>>> G = nx.complete_multipartite_graph(1, 2, 3)
>>> [G.nodes[u]['subset'] for u in G]
[0, 1, 1, 2, 2, 2]
>>> list(G.edges(0))
[(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)]
>>> list(G.edges(2))
[(2, 0), (2, 3), (2, 4), (2, 5)]
>>> list(G.edges(4))
[(4, 0), (4, 1), (4, 2)]
>>> G = nx.complete_multipartite_graph('a', 'bc', 'def')
>>> [G.nodes[u]['subset'] for u in sorted(G)]
[0, 1, 1, 2, 2, 2]


This function generalizes several other graph generator functions.

  • If no subset sizes are given, this returns the null graph.
  • If a single subset size n is given, this returns the empty graph on n nodes.
  • If two subset sizes m and n are given, this returns the complete bipartite graph on m + n nodes.
  • If subset sizes 1 and n are given, this returns the star graph on n + 1 nodes.

See also