human
Complete the below
@not_implemented_for('directed')
def min_weighted_dominating_set(G, weight=None):

    ''''Returns a dominating set that approximates the minimum weight node
    dominating set.
    Parameters
    G : NetworkX graph
    Undirected graph.
    weight : string
    The node attribute storing the weight of an edge. If provided,
    the node attribute with this key must be a number for each
    node. If not provided, each node is assumed to have weight one.
    Returns
    min_weight_dominating_set : set
    A set of nodes, the sum of whose weights is no more than `(\log
    w(V)) w(V^*)`, where `w(V)` denotes the sum of the weights of
    each node in the graph and `w(V^*)` denotes the sum of the
    weights of each node in the minimum weight dominating set.
    Notes
    This algorithm computes an approximate minimum weighted dominating
    set for the graph `G`. The returned solution has weight `(\log
    w(V)) w(V^*)`, where `w(V)` denotes the sum of the weights of each
    node in the graph and `w(V^*)` denotes the sum of the weights of
    each node in the minimum weight dominating set for the graph.
    This implementation of the algorithm runs in `O(m)` time, where `m`
    is the number of edges in the graph.
    References
    .. [1] Vazirani, Vijay V.
    *Approximation Algorithms*.
    Springer Science & Business Media, 2001.'
    '''
assistant
#Here is the Python code you requested.
    if (len(G) == 0):
        return set()
    dom_set = set()
    def _cost(node_and_neighborhood):
        'Returns    the    cost-effectiveness    of    greedily    choosing    the    given\n                                node.\n\n                                `node_and_neighborhood`    is    a    two-tuple    comprising    a    node    and    its\n                                closed    neighborhood.\n\n                                '
        (v, neighborhood) = node_and_neighborhood
        return (G.node[v].get(weight, 1) / len((neighborhood - dom_set)))
    vertices = set(G)
    neighborhoods = {v: ({v} | set(G[v])) for v in G}
    while vertices:
        (dom_node, min_set) = min(neighborhoods.items(), key=_cost)
        dom_set.add(dom_node)
        del neighborhoods[dom_node]
        vertices -= min_set
    return dom_set