Networkx outputs scipy sparse incidence matrices
Networkx also has it’s own flow solvers, but cvxpy gives you some interesting flexibility, like turning the problem mixed integer, quadratic terms, and other goodies. Plus it is very easy to get going as you’ll see.
So here’s a basic example of putting these two together. Very straightforward and cool.
import networkx as nx import cvxpy as cvx import matplotlib.pyplot as plt import numpy as np from scipy.sparse import lil_matrix #graph is an networkx graph from somewhere #print(edgedict) nEdges = len(graph.edges) nNodes = len(graph.nodes) posflow = cvx.Variable(nEdges) negflow = cvx.Variable(nEdges) # split flow into positive and negative parts so we can talk about absolute value. # Perhaps I should let cvxpy do it for me constraints = [ 0 <= posflow, 0 <= negflow ] absflow = posflow + negflow flow = posflow - negflow L = nx.incidence_matrix(graph, oriented=True ) source = np.zeros(nNodes) #lil_matrix(n_nodes) # just some random source placement. source = 1 source = -1 # cvxpy needs sparse matrices wrapped. Lcvx = cvx.Constant(L) #sourcecvx = cvx.Constant(source) # flow conservation constraints.append(Lcvx*flow == source) # can put other funky inequality constraints on things. objective = cvx.Minimize(cvx.sum(absflow)) print("building problem") prob = cvx.Problem(objective, constraints) print("starting solve") prob.solve(solver=cvx.OSQP, verbose = True) #or try cvx.CBC, cvx.CVXOPT, cvx.GLPK, others np.set_printoptions(threshold=np.inf) print(absflow.value)
Here was a cool visual from a multi commodity flow problem (nx.draw_networkx_edges)