def maximum_weighted_independent_set(G, weight=None, sampler=None, lagrange=2.0, **sampler_args):
    """Returns an approximate maximum weighted independent set.

    Defines a QUBO with ground states corresponding to a
    maximum weighted independent set and uses the sampler to sample
    from it.

    An independent set is a set of nodes such that the subgraph
    of G induced by these nodes contains no edges. A maximum
    independent set is an independent set of maximum total node weight.

    Parameters
    ----------
    G : NetworkX graph
        The graph on which to find a maximum cut weighted independent set.

    weight : string, optional (default None)
        If None, every node has equal weight. If a string, use this node
        attribute as the node weight. A node without this attribute is
        assumed to have max weight.

    sampler
        A binary quadratic model sampler. A sampler is a process that
        samples from low energy states in models defined by an Ising
        equation or a Quadratic Unconstrained Binary Optimization
        Problem (QUBO). A sampler is expected to have a 'sample_qubo'
        and 'sample_ising' method. A sampler is expected to return an
        iterable of samples, in order of increasing energy. If no
        sampler is provided, one must be provided using the
        `set_default_sampler` function.
        
    lagrange : optional (default 2)
        Lagrange parameter to weight constraints (no edges within set) 
        versus objective (largest set possible).

    sampler_args
        Additional keyword parameters are passed to the sampler.

    Returns
    -------
    indep_nodes : list
       List of nodes that form a maximum weighted independent set, as
       determined by the given sampler.

    Notes
    -----
    Samplers by their nature may not return the optimal solution. This
    function does not attempt to confirm the quality of the returned
    sample.

    References
    ----------

    `Independent Set on Wikipedia <https://en.wikipedia.org/wiki/Independent_set_(graph_theory)>`_

    `QUBO on Wikipedia <https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization>`_

    .. [AL] Lucas, A. (2014). Ising formulations of many NP problems.
       Frontiers in Physics, Volume 2, Article 5.

    """
    # Get a QUBO representation of the problem
    Q = maximum_weighted_independent_set_qubo(G, weight, lagrange)

    # use the sampler to find low energy states
    response = sampler.sample_qubo(Q, **sampler_args)

    # we want the lowest energy sample
    sample = next(iter(response))

    # nodes that are spin up or true are exactly the ones in S.
    return [node for node in sample if sample[node] > 0]
Returns an approximate maximum weighted independent set.

    Defines a QUBO with ground states corresponding to a
    maximum weighted independent set and uses the sampler to sample
    from it.

    An independent set is a set of nodes such that the subgraph
    of G induced by these nodes contains no edges. A maximum
    independent set is an independent set of maximum total node weight.

    Parameters
    ----------
    G : NetworkX graph
        The graph on which to find a maximum cut weighted independent set.

    weight : string, optional (default None)
        If None, every node has equal weight. If a string, use this node
        attribute as the node weight. A node without this attribute is
        assumed to have max weight.

    sampler
        A binary quadratic model sampler. A sampler is a process that
        samples from low energy states in models defined by an Ising
        equation or a Quadratic Unconstrained Binary Optimization
        Problem (QUBO). A sampler is expected to have a 'sample_qubo'
        and 'sample_ising' method. A sampler is expected to return an
        iterable of samples, in order of increasing energy. If no
        sampler is provided, one must be provided using the
        `set_default_sampler` function.
        
    lagrange : optional (default 2)
        Lagrange parameter to weight constraints (no edges within set) 
        versus objective (largest set possible).

    sampler_args
        Additional keyword parameters are passed to the sampler.

    Returns
    -------
    indep_nodes : list
       List of nodes that form a maximum weighted independent set, as
       determined by the given sampler.

    Notes
    -----
    Samplers by their nature may not return the optimal solution. This
    function does not attempt to confirm the quality of the returned
    sample.

    References
    ----------

    `Independent Set on Wikipedia <https://en.wikipedia.org/wiki/Independent_set_(graph_theory)>`_

    `QUBO on Wikipedia <https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization>`_

    .. [AL] Lucas, A. (2014). Ising formulations of many NP problems.
       Frontiers in Physics, Volume 2, Article 5.