maximal_independent_set

maximal_independent_set(G, nodes=None, seed=None)

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.

Parameters:

GNetworkX graph

nodeslist or iterable

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

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

Returns:

indep_nodeslist

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.

NetworkXNotImplemented

If G is directed.

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]