Source code for networkx.algorithms.mis

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"]

[docs] @not_implemented_for("directed") @py_random_state(2) @nx._dispatchable 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