77 lines
2.3 KiB
Python
77 lines
2.3 KiB
Python
"""
|
|
Algorithm to find a maximal (not maximum) independent set.
|
|
|
|
"""
|
|
import networkx as nx
|
|
from networkx.utils import not_implemented_for, py_random_state
|
|
|
|
__all__ = ["maximal_independent_set"]
|
|
|
|
|
|
@py_random_state(2)
|
|
@not_implemented_for("directed")
|
|
def 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
|
|
----------
|
|
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 :ref:`Randomness<randomness>`.
|
|
|
|
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.
|
|
|
|
NetworkXNotImplemented
|
|
If `G` is directed.
|
|
|
|
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 = {seed.choice(list(G))}
|
|
else:
|
|
nodes = set(nodes)
|
|
if not nodes.issubset(G):
|
|
raise nx.NetworkXUnfeasible(f"{nodes} is not a subset of the nodes of G")
|
|
neighbors = set.union(*[set(G.adj[v]) for v in nodes])
|
|
if set.intersection(neighbors, nodes):
|
|
raise nx.NetworkXUnfeasible(f"{nodes} is not an independent set of G")
|
|
indep_nodes = list(nodes)
|
|
available_nodes = set(G.nodes()).difference(neighbors.union(nodes))
|
|
while available_nodes:
|
|
node = seed.choice(list(available_nodes))
|
|
indep_nodes.append(node)
|
|
available_nodes.difference_update(list(G.adj[node]) + [node])
|
|
return indep_nodes
|