maximal_independent_set¶

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

Return 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.

Parameters:

G : NetworkX graph

nodes : list or iterable

Nodes that must be part of the independent set. This set of nodes must be independent.

Returns:

indep_nodes : list

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

Raises:

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.

Notes

This algorithm does not solve the maximum independent set problem.

Examples

>>> G = nx.path_graph(5)
>>> nx.maximal_independent_set(G) 
[4, 0, 2]
>>> nx.maximal_independent_set(G, [1]) 
[1, 3]