def test_negative_selfloops(self):
        """Negative selfloops should cause an exception if uncapacitated and
        always be saturated otherwise.
        """
        G = nx.DiGraph()
        G.add_edge(1, 1, weight=-1)
        assert_raises(nx.NetworkXUnbounded, nx.network_simplex, G)
        assert_raises(nx.NetworkXUnbounded, nx.capacity_scaling, G)
        G[1][1]['capacity'] = 2
        flowCost, H = nx.network_simplex(G)
        assert_equal(flowCost, -2)
        assert_equal(H, {1: {1: 2}})
        flowCost, H = nx.capacity_scaling(G)
        assert_equal(flowCost, -2)
        assert_equal(H, {1: {1: 2}})

        G = nx.MultiDiGraph()
        G.add_edge(1, 1, 'x', weight=-1)
        G.add_edge(1, 1, 'y', weight=1)
        assert_raises(nx.NetworkXUnbounded, nx.network_simplex, G)
        assert_raises(nx.NetworkXUnbounded, nx.capacity_scaling, G)
        G[1][1]['x']['capacity'] = 2
        flowCost, H = nx.network_simplex(G)
        assert_equal(flowCost, -2)
        assert_equal(H, {1: {1: {'x': 2, 'y': 0}}})
        flowCost, H = nx.capacity_scaling(G)
        assert_equal(flowCost, -2)
        assert_equal(H, {1: {1: {'x': 2, 'y': 0}}})

    def test_digraph1(self):
        # From Bradley, S. P., Hax, A. C. and Magnanti, T. L. Applied
        # Mathematical Programming. Addison-Wesley, 1977.
        G = nx.DiGraph()
        G.add_node(1, demand=-20)
        G.add_node(4, demand=5)
        G.add_node(5, demand=15)
        G.add_edges_from([(1, 2, {'capacity': 15, 'weight': 4}),
                          (1, 3, {'capacity': 8, 'weight': 4}),
                          (2, 3, {'weight': 2}),
                          (2, 4, {'capacity': 4, 'weight': 2}),
                          (2, 5, {'capacity': 10, 'weight': 6}),
                          (3, 4, {'capacity': 15, 'weight': 1}),
                          (3, 5, {'capacity': 5, 'weight': 3}),
                          (4, 5, {'weight': 2}),
                          (5, 3, {'capacity': 4, 'weight': 1})])
        flowCost, H = nx.network_simplex(G)
        soln = {1: {2: 12, 3: 8},
                2: {3: 8, 4: 4, 5: 0},
                3: {4: 11, 5: 5},
                4: {5: 10},
                5: {3: 0}}
        assert_equal(flowCost, 150)
        assert_equal(nx.min_cost_flow_cost(G), 150)
        assert_equal(H, soln)
        assert_equal(nx.min_cost_flow(G), soln)
        assert_equal(nx.cost_of_flow(G, H), 150)

        flowCost, H = nx.capacity_scaling(G)
        assert_equal(flowCost, 150)
        assert_equal(H, soln)
        assert_equal(nx.cost_of_flow(G, H), 150)

    def test_digon(self):
        """Check if digons are handled properly. Taken from ticket
        #618 by arv."""
        nodes = [(1, {}),
                 (2, {'demand': -4}),
                 (3, {'demand': 4}),
                 ]
        edges = [(1, 2, {'capacity': 3, 'weight': 600000}),
                 (2, 1, {'capacity': 2, 'weight': 0}),
                 (2, 3, {'capacity': 5, 'weight': 714285}),
                 (3, 2, {'capacity': 2, 'weight': 0}),
                 ]
        G = nx.DiGraph(edges)
        G.add_nodes_from(nodes)
        flowCost, H = nx.network_simplex(G)
        soln = {1: {2: 0},
                2: {1: 0, 3: 4},
                3: {2: 0}}
        assert_equal(flowCost, 2857140)
        assert_equal(nx.min_cost_flow_cost(G), 2857140)
        assert_equal(H, soln)
        assert_equal(nx.min_cost_flow(G), soln)
        assert_equal(nx.cost_of_flow(G, H), 2857140)

        flowCost, H = nx.capacity_scaling(G)
        assert_equal(flowCost, 2857140)
        assert_equal(H, soln)
        assert_equal(nx.cost_of_flow(G, H), 2857140)

    def run_random_trial(self):
        G = nx.MultiDiGraph()
        nodes = range(1, 10)
        edges = generate_edges(nodes, 50)
        G.add_edges_from(edges)
        source = random.choice(G.nodes())
        while True:
            target = random.choice(G.nodes())
            if target != source:
                break
        amount = random.randint(1, 10)
        G.node[source]['demand'] = -amount
        G.node[target]['demand'] = amount

        cost, flow_dict, exception = None, None, None
        try:
            cost, flow_dict = min_cost_flow(G)
        except nx.NetworkXException as e:
            exception = e

        H = unmulti(G)
        try:
            cost2, flow_dict2 = nx.network_simplex(H)
        except nx.NetworkXException as e:
            self.assertEquals(type(e) != type(exception))
            self.assertEquals(cost, None)
        else:
            self.assertEquals(cost, cost2)
            self.assertEquals(exception, None)

    def test_zero_capacity_edges(self):
        """Address issue raised in ticket #617 by arv."""
        G = nx.DiGraph()
        G.add_edges_from([(1, 2, {'capacity': 1, 'weight': 1}),
                          (1, 5, {'capacity': 1, 'weight': 1}),
                          (2, 3, {'capacity': 0, 'weight': 1}),
                          (2, 5, {'capacity': 1, 'weight': 1}),
                          (5, 3, {'capacity': 2, 'weight': 1}),
                          (5, 4, {'capacity': 0, 'weight': 1}),
                          (3, 4, {'capacity': 2, 'weight': 1})])
        G.nodes[1]['demand'] = -1
        G.nodes[2]['demand'] = -1
        G.nodes[4]['demand'] = 2

        flowCost, H = nx.network_simplex(G)
        soln = {1: {2: 0, 5: 1},
                2: {3: 0, 5: 1},
                3: {4: 2},
                4: {},
                5: {3: 2, 4: 0}}
        assert_equal(flowCost, 6)
        assert_equal(nx.min_cost_flow_cost(G), 6)
        assert_equal(H, soln)
        assert_equal(nx.min_cost_flow(G), soln)
        assert_equal(nx.cost_of_flow(G, H), 6)

        flowCost, H = nx.capacity_scaling(G)
        assert_equal(flowCost, 6)
        assert_equal(H, soln)
        assert_equal(nx.cost_of_flow(G, H), 6)

 def test_large(self):
     fname = os.path.join(os.path.dirname(__file__), 'netgen-2.gpickle.bz2')
     G = nx.read_gpickle(fname)
     flowCost, flowDict = nx.network_simplex(G)
     assert_equal(6749969302, flowCost)
     assert_equal(6749969302, nx.cost_of_flow(G, flowDict))
     flowCost, flowDict = nx.capacity_scaling(G)
     assert_equal(6749969302, flowCost)
     assert_equal(6749969302, nx.cost_of_flow(G, flowDict))

    def test_multidigraph(self):
        """Multidigraphs are acceptable."""
        G = nx.MultiDiGraph()
        G.add_weighted_edges_from([(1, 2, 1), (2, 3, 2)], weight='capacity')
        flowCost, H = nx.network_simplex(G)
        assert_equal(flowCost, 0)
        assert_equal(H, {1: {2: {0: 0}}, 2: {3: {0: 0}}, 3: {}})

        flowCost, H = nx.capacity_scaling(G)
        assert_equal(flowCost, 0)
        assert_equal(H, {1: {2: {0: 0}}, 2: {3: {0: 0}}, 3: {}})

def processWiki(page, p=None, ignoreConditionalProbabilities=False):
    if p == None: p = readDict("data/wpairs")
    pe = readCounts("data/unigram-counts/" + page + ".en.tok.ucounts")
    pf = readCounts("data/unigram-counts/" + page + ".fr.tok.ucounts")

    G = nx.DiGraph()
    # 1 is source (F), 2 is sink (E)
    # 3 is F-null, 4 is E-null

    G.add_node(1, {'demand': -1, 'name': '*SOURCE*'})
    G.add_node(2, {'demand':  1, 'name': '*SINK*'})
    G.add_node(3, {'name': '*F-NULL*'})
    G.add_node(4, {'name': '*E-NULL*'})

    G.add_edge(1, 3, {'capacity': 1, 'weight': 100000})
    G.add_edge(4, 2, {'capacity': 1, 'weight': 100000})

    nCnt = 5

    fID = {}
    for f in pf.iterkeys():
        fID[f] = nCnt
        G.add_node(nCnt, {'name': f, 'lang': 'f'})
        G.add_edge(1, nCnt, {'capacity': pf[f], 'weight': 1})
        G.add_edge(nCnt, 4, {'capacity': 1, 'weight': 100000})
        nCnt += 1

    eID = {}
    for e in pe.iterkeys():
        eID[e] = nCnt
        G.add_node(nCnt, {'name': e, 'lang': 'e'})
        G.add_edge(nCnt, 2, {'capacity': pe[e], 'weight': 1})
        G.add_edge(3, nCnt, {'capacity': 1, 'weight': 100000})
        nCnt += 1

    for f in pf.iterkeys():
        nf = fID[f]
        if p.has_key(f):
            for e in p[f].iterkeys():
                if eID.has_key(e):
                    ne = eID[e]
                    cap = p[f][e]
                    if ignoreConditionalProbabilities: cap = 1
                    G.add_edge(nf, ne, {'capacity': cap, 'weight': 1})
                    
    flowCost,flowDict = nx.network_simplex(G)

    return G,flowDict

    def match(self, riders, ridees):
        graph = nx.DiGraph()
        for rider in riders:
            graph.add_node(rider.household_id, demand = - rider.capacity)

        for ridee in ridees:
            graph.add_node(ridee.household_id, demand = 1)

        for rider in riders:
            for ridee in ridees:
                distance = this._get_distance(rider.location, ridee.location)
                graph.add_edge(rider.household_id, ridee.household_id, weight = distance, capacity = 1)

        flowCost, flowDict = nx.network_simplex(graph)

        return flowDict

def nxMCF(startNodes, endNodes, capacities, costs, supplies):
    G = nx.DiGraph()
    for n, s in enumerate(supplies):
        G.add_node(n, demand=-s)

    for edgei in range(len(startNodes)):
        G.add_edge(startNodes[edgei],
                   endNodes[edgei],
                   weight=costs[edgei],
                   capacity=capacities[edgei])

    cost, flow = nx.network_simplex(G, demand='demand', capacity='capacity', weight='weight')
    totalFlow = 0
    for k1,v1 in flow.items():
        for k2,v2 in v1.items():
            totalFlow += v2
    return cost, totalFlow

    def test_transshipment(self):
        G = nx.DiGraph()
        G.add_node('a', demand=1)
        G.add_node('b', demand=-2)
        G.add_node('c', demand=-2)
        G.add_node('d', demand=3)
        G.add_node('e', demand=-4)
        G.add_node('f', demand=-4)
        G.add_node('g', demand=3)
        G.add_node('h', demand=2)
        G.add_node('r', demand=3)
        G.add_edge('a', 'c', weight=3)
        G.add_edge('r', 'a', weight=2)
        G.add_edge('b', 'a', weight=9)
        G.add_edge('r', 'c', weight=0)
        G.add_edge('b', 'r', weight=-6)
        G.add_edge('c', 'd', weight=5)
        G.add_edge('e', 'r', weight=4)
        G.add_edge('e', 'f', weight=3)
        G.add_edge('h', 'b', weight=4)
        G.add_edge('f', 'd', weight=7)
        G.add_edge('f', 'h', weight=12)
        G.add_edge('g', 'd', weight=12)
        G.add_edge('f', 'g', weight=-1)
        G.add_edge('h', 'g', weight=-10)
        flowCost, H = nx.network_simplex(G)
        soln = {'a': {'c': 0},
                'b': {'a': 0, 'r': 2},
                'c': {'d': 3},
                'd': {},
                'e': {'r': 3, 'f': 1},
                'f': {'d': 0, 'g': 3, 'h': 2},
                'g': {'d': 0},
                'h': {'b': 0, 'g': 0},
                'r': {'a': 1, 'c': 1}}
        assert_equal(flowCost, 41)
        assert_equal(nx.min_cost_flow_cost(G), 41)
        assert_equal(H, soln)
        assert_equal(nx.min_cost_flow(G), soln)
        assert_equal(nx.cost_of_flow(G, H), 41)

        flowCost, H = nx.capacity_scaling(G)
        assert_equal(flowCost, 41)
        assert_equal(nx.cost_of_flow(G, H), 41)
        assert_equal(H, soln)

 def test_simple_digraph(self):
     G = nx.DiGraph()
     G.add_node('a', demand = -5)
     G.add_node('d', demand = 5)
     G.add_edge('a', 'b', weight = 3, capacity = 4)
     G.add_edge('a', 'c', weight = 6, capacity = 10)
     G.add_edge('b', 'd', weight = 1, capacity = 9)
     G.add_edge('c', 'd', weight = 2, capacity = 5)
     flowCost, H = nx.network_simplex(G)
     soln = {'a': {'b': 4, 'c': 1},
             'b': {'d': 4},
             'c': {'d': 1},
             'd': {}}
     assert_equal(flowCost, 24)
     assert_equal(nx.min_cost_flow_cost(G), 24)
     assert_equal(H, soln)
     assert_equal(nx.min_cost_flow(G), soln)
     assert_equal(nx.cost_of_flow(G, H), 24)

 def test_bone_shaped(self):
     # From #1283
     G = nx.DiGraph()
     G.add_node(0, demand=-4)
     G.add_node(1, demand=2)
     G.add_node(2, demand=2)
     G.add_node(3, demand=4)
     G.add_node(4, demand=-2)
     G.add_node(5, demand=-2)
     G.add_edge(0, 1, capacity=4)
     G.add_edge(0, 2, capacity=4)
     G.add_edge(4, 3, capacity=4)
     G.add_edge(5, 3, capacity=4)
     G.add_edge(0, 3, capacity=0)
     flowCost, H = nx.network_simplex(G)
     assert_equal(flowCost, 0)
     assert_equal(
         H, {0: {1: 2, 2: 2, 3: 0}, 1: {}, 2: {}, 3: {}, 4: {3: 2}, 5: {3: 2}})
     flowCost, H = nx.capacity_scaling(G)
     assert_equal(flowCost, 0)
     assert_equal(
         H, {0: {1: 2, 2: 2, 3: 0}, 1: {}, 2: {}, 3: {}, 4: {3: 2}, 5: {3: 2}})

    nz_idx = pd.Series(np.nonzero(C_transfers.values)[0])
    for i in range(abs(dif)):
        C_transfers.iloc[nz_idx[i]] -= direct 

for i in CG.nodes():
    CG.node[i]['load'] = C_loads[i]
    CG.node[i]['gen'] = C_gen[i]
    CG.node[i]['trans'] = C_transfers[i]

for i in CG.nodes():
    CG.node[i]['MW_net'] = CG.node[i]['gen'] - CG.node[i]['load'] - CG.node[i]['trans']

DG = CG.to_directed()


NS = nx.network_simplex(DG, demand='MW_net', weight='R', capacity='tot_MW_cap')
#### EVERYTHING BELOW DOESN'T WORK!!!

for i in G.nodes():
    kv_list = [G.adj[i][j]['tot_kv'] for j in G.adj[i].keys() if isinstance(j, int)]
    kv_max, kv_min = max(kv_list), min(kv_list)
    G[i]['max_volt'] = kv_max
    G[i]['min_volt'] = kv_min

#### GET GRID VOLTAGES FROM EIA FORM DATA

mwkv = pd.DataFrame(np.zeros(len(G.nodes())), index=G.nodes())

for x in ['load', 'gen', 'trans', 'min_volt', 'max_volt']:
    mwkv_col = pd.DataFrame(np.vstack([tuple([i, G[i][x]]) for i in G.nodes() if x in G[i].keys()])).rename(columns={1 : x}).set_index(0)
    mwkv = pd.concat([mwkv, mwkv_col], axis=1)

G.add_node(1, demand=-2)
G.add_node(2, demand=-5)
# Adiciona nos de demanda
G.add_node(3, demand=1)
G.add_node(4, demand=3)
G.add_node(5, demand=3)
# Adiciona os arcos
G.add_edge(1, 3, weight=3)
G.add_edge(2, 3, weight=7)
# ###################################
G.add_edge(1, 4, weight=4)
G.add_edge(2, 4, weight=2)
# ###################################
G.add_edge(1, 5, weight=1)
G.add_edge(2, 5, weight=5)
flowCost, flowDict = nx.network_simplex(G)
print flowCost
# print flowDict
k,w = 0,0
mat = np.zeros([2,3])
cost = np.zeros([2,3])
total = 0
for i in flowDict:
    #print "i:%d\n"%i
    w = 0
    for j in flowDict[i]:
        # print flowDict[i][j],
        mat[k,w] = flowDict[i][j]
        cost[k,w] = G[i][j]["weight"]
        w += 1
        total += flowDict[i][j]*G[i][j]["weight"]

def rig_component(G, x, y, maxW):
    """ Compute the RIG metric on a single component.

    Parameters
    ----------
    G : nx.Graph
       A connected graph of weighted edges
    x : pd.Series
       Vector of nodes and their abundance in sample x
       within the connected graph G
    y : pd.Series
       Vector of nodes and their abundance in sample y
       within the connected graph G
    maxW : float
       The cost of an insertion step

    Returns
    -------
    float :
       Distance between sample x and sample y

    Note
    ----
    If x or y is None, then 1 will be added to the total distance.
    If they are both None, then the distance will be zero.
    Also, the weights of the edges must be contained in `'weight'`.
    """

    # Both samples don't contain any metabolites
    if len(x) == 0 and len(y) == 0:
        return 0
    xtotal = int(max([x.sum(), 1]))
    ytotal = int(max([y.sum(), 1]))

    # Convert everything to fractions
    if x.sum() != 0:
        x = pd.Series([Fraction(i, xtotal) for i in np.ravel(x.values)], index=x.index)
    if y.sum() != 0:
        y = pd.Series([Fraction(i, ytotal) for i in np.ravel(y.values)], index=y.index)
    if x.equals(y):
        return 0

    # The component being analyzed has only 1 node.
    # So the networkx simplex algorithm cannot be run
    # since there are no edges.
    if len(list(G.nodes())) == 1:
        return maxW

    cost = 0
    edges = G.edges(data="weight")

    # If there one of the samples doesn't have any metabolites
    # on the component, arbituarily pick two metabolites
    # and append them to the set.  This to address the issue of
    # measuring distance between unshared components.
    if len(x) == 0 or x.sum() == 0:
        x = pd.Series({y.index[0]: Fraction(1, 1)})
        weight = maxW
    elif len(y) == 0 or y.sum() == 0:
        y = pd.Series({x.index[0]: Fraction(1, 1)})
        weight = maxW
    else:
        weight = 0
    _G = copy.deepcopy(G)

    xarr = pd.Series({n: (x[n] if n in x else 0) for n in G.nodes()})
    yarr = pd.Series({n: (y[n] if n in y else 0) for n in G.nodes()})

    d = 0
    maxxD = max(map(lambda k: k.denominator, x))
    maxyD = max(map(lambda k: k.denominator, y))

    for node in _G.nodes():
        dmd = int((xarr[node] - yarr[node]) * xtotal * ytotal)
        _G.node[node]["demand"] = dmd
        d += dmd

    W, _ = nx.network_simplex(_G.to_directed())
    cost += W + weight
    return cost

def min_cost_flow(G, demand = 'demand', capacity = 'capacity',
                  weight = 'weight'):
    r"""Return a minimum cost flow satisfying all demands in digraph G.

    G is a digraph with edge costs and capacities and in which nodes
    have demand, i.e., they want to send or receive some amount of
    flow. A negative demand means that the node wants to send flow, a
    positive demand means that the node want to receive flow. A flow on
    the digraph G satisfies all demand if the net flow into each node
    is equal to the demand of that node.

    Parameters
    ----------
    G : NetworkX graph
        DiGraph on which a minimum cost flow satisfying all demands is
        to be found.

    demand : string
        Nodes of the graph G are expected to have an attribute demand
        that indicates how much flow a node wants to send (negative
        demand) or receive (positive demand). Note that the sum of the
        demands should be 0 otherwise the problem in not feasible. If
        this attribute is not present, a node is considered to have 0
        demand. Default value: 'demand'.

    capacity : string
        Edges of the graph G are expected to have an attribute capacity
        that indicates how much flow the edge can support. If this
        attribute is not present, the edge is considered to have
        infinite capacity. Default value: 'capacity'.

    weight : string
        Edges of the graph G are expected to have an attribute weight
        that indicates the cost incurred by sending one unit of flow on
        that edge. If not present, the weight is considered to be 0.
        Default value: 'weight'.

    Returns
    -------
    flowDict : dictionary
        Dictionary of dictionaries keyed by nodes such that
        flowDict[u][v] is the flow edge (u, v).

    Raises
    ------
    NetworkXError
        This exception is raised if the input graph is not directed or
        not connected.

    NetworkXUnfeasible
        This exception is raised in the following situations:

            * The sum of the demands is not zero. Then, there is no
              flow satisfying all demands.
            * There is no flow satisfying all demand.

    NetworkXUnbounded
        This exception is raised if the digraph G has a cycle of
        negative cost and infinite capacity. Then, the cost of a flow
        satisfying all demands is unbounded below.

    See also
    --------
    cost_of_flow, max_flow_min_cost, min_cost_flow_cost, network_simplex

    Examples
    --------
    A simple example of a min cost flow problem.

    >>> import networkx as nx
    >>> G = nx.DiGraph()
    >>> G.add_node('a', demand = -5)
    >>> G.add_node('d', demand = 5)
    >>> G.add_edge('a', 'b', weight = 3, capacity = 4)
    >>> G.add_edge('a', 'c', weight = 6, capacity = 10)
    >>> G.add_edge('b', 'd', weight = 1, capacity = 9)
    >>> G.add_edge('c', 'd', weight = 2, capacity = 5)
    >>> flowDict = nx.min_cost_flow(G)
    """
    return nx.network_simplex(G, demand = demand, capacity = capacity,
                              weight = weight)[1]

def min_cost_flow_cost(G, demand='demand', capacity='capacity',
                       weight='weight'):
    r"""Find the cost of a minimum cost flow satisfying all demands in digraph G.

    G is a digraph with edge costs and capacities and in which nodes
    have demand, i.e., they want to send or receive some amount of
    flow. A negative demand means that the node wants to send flow, a
    positive demand means that the node want to receive flow. A flow on
    the digraph G satisfies all demand if the net flow into each node
    is equal to the demand of that node.

    Parameters
    ----------
    G : NetworkX graph
        DiGraph on which a minimum cost flow satisfying all demands is
        to be found.

    demand : string
        Nodes of the graph G are expected to have an attribute demand
        that indicates how much flow a node wants to send (negative
        demand) or receive (positive demand). Note that the sum of the
        demands should be 0 otherwise the problem in not feasible. If
        this attribute is not present, a node is considered to have 0
        demand. Default value: 'demand'.

    capacity : string
        Edges of the graph G are expected to have an attribute capacity
        that indicates how much flow the edge can support. If this
        attribute is not present, the edge is considered to have
        infinite capacity. Default value: 'capacity'.

    weight : string
        Edges of the graph G are expected to have an attribute weight
        that indicates the cost incurred by sending one unit of flow on
        that edge. If not present, the weight is considered to be 0.
        Default value: 'weight'.

    Returns
    -------
    flowCost : integer, float
        Cost of a minimum cost flow satisfying all demands.

    Raises
    ------
    NetworkXError
        This exception is raised if the input graph is not directed or
        not connected.

    NetworkXUnfeasible
        This exception is raised in the following situations:

            * The sum of the demands is not zero. Then, there is no
              flow satisfying all demands.
            * There is no flow satisfying all demand.

    NetworkXUnbounded
        This exception is raised if the digraph G has a cycle of
        negative cost and infinite capacity. Then, the cost of a flow
        satisfying all demands is unbounded below.

    See also
    --------
    cost_of_flow, max_flow_min_cost, min_cost_flow, network_simplex

    Notes
    -----
    This algorithm is not guaranteed to work if edge weights or demands
    are floating point numbers (overflows and roundoff errors can
    cause problems). As a workaround you can use integer numbers by
    multiplying the relevant edge attributes by a convenient
    constant factor (eg 100).

    Examples
    --------
    A simple example of a min cost flow problem.

    >>> import networkx as nx
    >>> G = nx.DiGraph()
    >>> G.add_node('a', demand = -5)
    >>> G.add_node('d', demand = 5)
    >>> G.add_edge('a', 'b', weight = 3, capacity = 4)
    >>> G.add_edge('a', 'c', weight = 6, capacity = 10)
    >>> G.add_edge('b', 'd', weight = 1, capacity = 9)
    >>> G.add_edge('c', 'd', weight = 2, capacity = 5)
    >>> flowCost = nx.min_cost_flow_cost(G)
    >>> flowCost
    24
    """
    return nx.network_simplex(G, demand=demand, capacity=capacity,
                              weight=weight)[0]