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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def maximal_matching(G, sampler=None, **sampler_args):
 """Finds an approximate maximal matching. Defines a QUBO with ground states corresponding to a maximal matching and uses the sampler to sample from it. A matching is a subset of edges in which no node occurs more than once. A maximal matching is one in which no edges from G can be added without violating the matching rule. Parameters G : NetworkX graph The graph on which to find a maximal matching. 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. sampler_args Additional keyword parameters are passed to the sampler. Returns ------- matching : set A maximal matching of the graph. 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 `Matching on Wikipedia <https://en.wikipedia.org/wiki/Matching_(graph_theory)>`_ `QUBO on Wikipedia <https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization>`_ Based on the formulation presented in [AL]_ """


    # the maximum degree
    delta = max(G.degree(node) for node in G)

    # use the maximum degree to determine the infeasible gaps
    A = 1.
    if delta == 2:
        B = .75
    else:
        B = .75 * A / (delta - 2.)  # we want A > (delta - 2) * B

    # each edge in G gets a variable, so let's create those
    edge_mapping = _edge_mapping(G)

    # build the QUBO
    Q = _maximal_matching_qubo(G, edge_mapping, magnitude=B)
    Qm = _matching_qubo(G, edge_mapping, magnitude=A)
    for edge, bias in Qm.items():
        if edge not in Q:
            Q[edge] = bias
        else:
            Q[edge] += bias

    # 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))

    # the matching are the edges that are 1 in the sample
    return set(edge for edge in G.edges if sample[edge_mapping[edge]] > 0)