maxflow: maximize flow from source to sink, taking into account arc capacities M
    Parameters:
        - V: set of vertices
        - M[i,j]: dictionary or capacity for arcs (i,j)
        - source: flow origin
        - sink: flow target
    Returns a model, ready to be solved.

def maxflow(V,M,source,sink):
    """maxflow: maximize flow from source to sink, taking into account arc capacities M
    Parameters:
        - V: set of vertices
        - M[i,j]: dictionary or capacity for arcs (i,j)
        - source: flow origin
        - sink: flow target
    Returns a model, ready to be solved.
        """
    # create max-flow underlying model, on which to find cuts
    model = Model("maxflow")
    
    f = {} # flow variable
    for (i,j) in M:
        f[i,j] = model.addVar(lb=-M[i,j], ub=M[i,j], name="flow(%s,%s)"%(i,j))

    cons = {}
    for i in V:
        if i != source and i != sink:
            cons[i] = model.addCons(
                quicksum(f[i,j] for j in V if i<j and (i,j) in M) - \
                quicksum(f[j,i] for j in V if i>j and (j,i) in M) == 0,
                "FlowCons(%s)"%i)

    model.setObjective(quicksum(f[i,j] for (i,j) in M if i==source), "maximize")

    # model.write("tmp.lp")
    model.data = f,cons
    return model