+ j|Rt^RIt^RIHtHtR.t]!R4]!^4]PRRl444tR#)z= Algorithm to find a maximal (not maximum) independent set. N)not_implemented_forpy_random_statemaximal_independent_setdirectedc V'gVP\V440pM \V4pVPV4'g\P !V R24h\P !VUu.uFp\VPV,4NK! up!p\PWA4'd\P !V R24h\V4p\VP44PVP V44pV'daVP\V44pVPV4VP\VPV,4V.,4KhV#uupi)a 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`. Returns ------- indep_nodes : set Set 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(4) >>> sorted(nx.maximal_independent_set(G, seed=1)) [1, 3] Note that a graph may have many maximal independent sets; for example, the path graph with 4 nodes has 3 maximal independent sets: ``{0, 2}``, ``{0, 3}`` and ``{1, 3}``. >>> sorted(nx.maximal_independent_set(G, seed=2)) [0, 2] This function returns a single maximal independent set. Enumerating *all* of the maximal independent sets in a graph can be achieved by enumerating the cliques in the complement graph: >>> sorted( ... sorted(c) ... for c in nx.enumerate_all_cliques(nx.complement(G)) ... if len(c) > 1 # Ignore cliques comprising a single node ... ) [[0, 2], [0, 3], [1, 3]] Note however that enumerating all cliques is exponential in the number of nodes in the worst case (e.g. the complete graph). The `nodes` keyword argument can be used to produce a maximal independent set that contains the given node(s): >>> sorted(nx.maximal_independent_set(G, nodes={1})) [1, 3] An exception is raised if `nodes` are not independent >>> nx.maximal_independent_set(G, nodes={1, 2}) Traceback (most recent call last): ... networkx.exception.NetworkXUnfeasible: {1, 2} is not an independent set of G Notes ----- This algorithm does not solve the maximum independent set problem. See Also -------- :func:`~networkx.algorithms.approximation.clique.maximum_independent_set` : Algorithm for approximating the maximum independent set, i.e. a maximal independent set of maximum cardinality. z" is not a subset of the nodes of Gz is not an independent set of G) choicelistsetissubsetnxNetworkXUnfeasibleunionadj intersectionnodes differenceadddifference_update)Grseedv neighbors indep_nodesavailable_nodesnodes&&& X/home/luca/screen-checking/.venv/lib/python3.14/site-packages/networkx/algorithms/mis.pyrr sp T!W%&E  >>!  ##ug-O$PQQ 595aCaM59:I  ))##ug-L$MNNe*K!'')n// 0FGO {{401))$quuT{*;tf*DE :s4%E>)NN) __doc__networkxr networkx.utilsrr__all__ _dispatchablerrr#sP ? $ %Z d!dr"