Warning

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

# Source code for networkx.algorithms.mis

# -*- coding: utf-8 -*-
# $Id: maximalIndependentSet.py 576 2011-03-01 05:50:34Z lleeoo$
"""
Algorithm to find a maximal (not maximum) independent set.

"""
#    Leo Lopes <leo.lopes@monash.edu>
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>

__author__ = "\n".join(["Leo Lopes <leo.lopes@monash.edu>",
"Loïc Séguin-C. <loicseguin@gmail.com>"])

__all__ = ['maximal_independent_set']

import random
import networkx as nx

[docs]def maximal_independent_set(G, nodes=None):
"""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.

Examples
--------
>>> 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]

Notes
------
This algorithm does not solve the maximum independent set problem.

"""
if not nodes:
nodes = set([random.choice(G.nodes())])
else:
nodes = set(nodes)
if not nodes.issubset(G):
raise nx.NetworkXUnfeasible(
"%s is not a subset of the nodes of G" % nodes)
neighbors = set.union(*[set(G.neighbors(v)) for v in nodes])
if set.intersection(neighbors, nodes):
raise nx.NetworkXUnfeasible(
"%s is not an independent set of G" % nodes)
indep_nodes = list(nodes)
available_nodes = set(G.nodes()).difference(neighbors.union(nodes))
while available_nodes:
node = random.choice(list(available_nodes))
indep_nodes.append(node)
available_nodes.difference_update(G.neighbors(node) + [node])
return indep_nodes