def define_edge_term(variable_dict, graph, edge, prefix="x",
                     perturb=False, max_weight=None):
    """ Define a single edge term in the objective """

    weight = graph_utils.get_edge_weight(graph, *edge)
    name = name_variable(edge, prefix=prefix)
    return compute_edge_term(weight, variable_dict[name])
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def compute_f3_edge(graph, vertex_a, vertex_b, self_max=False):
    """ Compute feature f3 of Sun et al. for a specific edge"""

    out_weights = graph_utils.get_edge_weights(graph, vertex_a)
    edge_weight = graph_utils.get_edge_weight(graph, vertex_a, vertex_b)
    if not self_max:
        numerator = edge_weight - np.mean(out_weights)
        denominator = np.max(out_weights) - np.min(out_weights)
    else:
        numerator = edge_weight - np.partition(out_weights, -2)[:-1].mean()
        denominator = np.partition(out_weights, -2)[-2] - np.min(out_weights)
    return numerator / denominator
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def compute_f2_edge(graph, vertex_a, vertex_b, self_max=False):
    """ Compute feature f2 of Sun et al. for a specific edge"""

    out_weights = graph_utils.get_edge_weights(graph, vertex_a)
    in_weights = graph_utils.get_edge_weights(graph, vertex_b, out=False)
    edge_weight = graph_utils.get_edge_weight(graph, vertex_a, vertex_b)
    numerator = edge_weight - np.min(out_weights)
    if not self_max:
        denominator = np.max(in_weights) - np.min(in_weights)
    else:
        denominator = np.partition(in_weights, -2)[-2] - np.min(in_weights)
    return numerator / denominator
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def compute_f1_edge(graph, vertex_a, vertex_b, self_max=False):
    """ Compute feature f1 of Sun et al. for a specific edge"""
    """ If the self-weight is the largest weight, set self_max true """

    out_weights = graph_utils.get_edge_weights(graph, vertex_a)
    edge_weight = graph_utils.get_edge_weight(graph, vertex_a, vertex_b)
    numerator = edge_weight - np.min(out_weights)
    if not self_max:
        denominator = np.max(out_weights) - np.min(out_weights)
    else:
        denominator = np.partition(out_weights, -2)[-2] - np.min(out_weights)
    return numerator / denominator
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def get_path_lengths(graph, path):
    """ Get an array of edge lengths for a path """

    edges = get_path_edges(path)
    return np.array(
        [graph_utils.get_edge_weight(graph, *edge) for edge in edges])
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    object = io_utils.optObject().read_from_file(file)
    graph = object.get_graph()
    graph = graph_utils.delete_self_weights(graph)
    graph = graph.to_undirected()
    
    solution = cc_solve.solution_from_path(file)
    edges = graph_utils.get_tour_edges(solution.tour)
    if np.min(solution.tour) < 1 and np.min(graph.nodes) > 0:
        edges += 1
    edges =  model.tuples_to_strings(edges)
    
    sparse_edges = model.run_sparsify(graph, 6)
    prune_edges = []
    for item in sparse_edges:
        prune_edges += list(item)
    prune_weights = [graph_utils.get_edge_weight(graph, *edge) for edge in prune_edges]
    prune_bunches = [(*edge, {"weight": weight}) for
                     (edge, weight) in zip(prune_edges, prune_weights)]
    
    g = nx.Graph()
    g.add_edges_from(prune_bunches)

    all_weights = []

    for mun, vertex in enumerate(graph.nodes):
        edges = [edge for edge in graph.edges if vertex in edge]
        weights = [9999999] * len(edges)
        for pum, edge in enumerate(edges):
            if edge in prune_edges:
                index = prune_edges.index(edge)
                weights[pum] = prune_weights[index]