def min_feedback_arc_set(edges, remove=False, maxcycles=20000):
    """
    A directed graph may contain directed cycles, when such cycles are
    undesirable, we wish to eliminate them and obtain a directed acyclic graph
    (DAG). A feedback arc set has the property that it has at least one edge
    of every cycle in the graph. A minimum feedback arc set is the set that
    minimizes the total weight of the removed edges; or alternatively maximize
    the remaining edges. See: <http://en.wikipedia.org/wiki/Feedback_arc_set>.

    The MIP formulation proceeds as follows: use 0/1 indicator variable to
    select whether an edge is in the set, subject to constraint that each cycle
    must pick at least one such edge.

    >>> g = [(1, 2, 2), (2, 3, 2), (3, 4, 2)] + [(1, 3, 1), (3, 2, 1), (2, 4, 1)]
    >>> min_feedback_arc_set(g)
    ([(3, 2, 1)], 1)
    >>> min_feedback_arc_set(g, remove=True)  # Return DAG
    ([(1, 2, 2), (2, 3, 2), (3, 4, 2), (1, 3, 1), (2, 4, 1)], 1)
    """
    G = nx.DiGraph()
    edge_to_index = {}
    for i, (a, b, w) in enumerate(edges):
        G.add_edge(a, b)
        edge_to_index[a, b] = i

    nedges = len(edges)
    L = LPInstance()

    L.add_objective(edges, objective=MINIMIZE)

    constraints = []
    ncycles = 0
    for c in nx.simple_cycles(G):
        cycle_edges = []
        rc = c + [c[0]]  # Rotate the cycle
        for a, b in pairwise(rc):
            cycle_edges.append(edge_to_index[a, b])
        cc = summation(cycle_edges)
        constraints.append("{0} >= 1".format(cc))
        ncycles += 1
        if ncycles == maxcycles:
            break
    logging.debug("A total of {0} cycles found.".format(ncycles))

    L.constraints = constraints
    L.add_vars(nedges)

    selected, obj_val = L.lpsolve(clean=False)
    if remove:
        results = [x for i, x in enumerate(edges) if i not in selected] \
            if selected else None
    else:
        results = [x for i, x in enumerate(edges) if i in selected] \
            if selected else None

    return results, obj_val