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maximal_independent_set(G, nodes=None, seed=None)[source]

Returns a random maximal independent set guaranteed to contain a given set of nodes.

An independent set is a set of nodes such that the subgraph of G induced by these nodes contains no edges. A maximal independent set is an independent set such that it is not possible to add a new node and still get an independent set.

  • G (NetworkX graph)
  • nodes (list or iterable) – Nodes that must be part of the independent set. This set of nodes must be independent.
  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

indep_nodes – List of nodes that are part of a maximal independent set.

Return type:


  • NetworkXUnfeasible – If the nodes in the provided list are not part of the graph or do not form an independent set, an exception is raised.
  • NetworkXNotImplemented – If G is directed.


>>> G = nx.path_graph(5)
>>> nx.maximal_independent_set(G) # doctest: +SKIP
[4, 0, 2]
>>> nx.maximal_independent_set(G, [1]) # doctest: +SKIP
[1, 3]


This algorithm does not solve the maximum independent set problem.