# A is the incidence matrix. 
# c is a vector of edge capacities.
flows = Variable(E-2)
source = Variable()
sink = Variable()
p = Problem(Maximize(source),
              [A*hstack([flows,source,sink]) == 0,
               0 <= flows,
               flows <= c])

class Edge(object):
    """ An undirected, capacity limited edge. """
    def __init__(self, capacity):
        self.capacity = capacity
        self.flow = Variable()

    # Connects two nodes via the edge.
    def connect(self, in_node, out_node):
        in_node.edge_flows.append(-self.flow)
        out_node.edge_flows.append(self.flow)

    # Returns the edge's internal constraints.
    def constraints(self):
        return [abs(self.flow) <= self.capacity]

class Node(object):
    """ A node with accumulation. """
    def __init__(self, accumulation=0):
        self.accumulation = accumulation
        self.edge_flows = []

    # Returns the node's internal constraints.
    def constraints(self):
        return [sum(f for f in self.edge_flows) == self.accumulation]

constraints = []
for obj in nodes + edges:
    constraints += obj.constraints()
prob = Problem(Maximize(sink.accumulation), constraints)