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>
#    All rights reserved.
#    BSD license.

__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