### view env/lib/python3.9/site-packages/networkx/algorithms/mis.py @ 0:4f3585e2f14bdraftdefaulttip

author shellac Mon, 22 Mar 2021 18:12:50 +0000
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"""
Algorithm to find a maximal (not maximum) independent set.

"""
import networkx as nx
from networkx.utils import not_implemented_for
from networkx.utils import 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, )  # 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)