CF84 CF84 - 1 month ago 13
Python Question

NetworkX: how to create an incidence matrix of a weighted graph?

Having created a grid network like this:

from __future__ import division
import networkx as nx
from pylab import *
import matplotlib.pyplot as plt
%pylab inline

ncols=10

N=10 #Nodes per side
G=nx.grid_2d_graph(N,N)
labels = dict( ((i,j), i + (N-1-j) * N ) for i, j in G.nodes() )
nx.relabel_nodes(G,labels,False)
inds=labels.keys()
vals=labels.values()
inds=[(N-j-1,N-i-1) for i,j in inds]
pos2=dict(zip(vals,inds))


And having assigned each edge a weight corresponding to its length (in this trivial case, all lenghts=1):

#Weights
from math import sqrt

weights = dict()
for source, target in G.edges():
x1, y1 = pos2[source]
x2, y2 = pos2[target]
weights[(source, target)] = round((math.sqrt((x2-x1)**2 + (y2-y1)**2)),3)

for e in G.edges():
G[e[0]][e[1]] = weights[e] #Assigning weights to G.edges()


This is what my
G.edges()
looks like: (startnode ID, endnode ID, weight)

[(0, 1, 1.0),
(0, 10, 1.0),
(1, 11, 1.0),
(1, 2, 1.0),... ] #Trivial case: all weights are unitary


How can I create an incidence matrix that takes into account the weights that have just been defined? I want to use
nx.incidence_matrix(G, nodelist=None, edgelist=None, oriented=False, weight=None)
, but what is the correct value for
weight
in this case?

The docs say that
weight
is a string representing "the edge data key used to provide each value in the matrix", but what does it mean specifically? I have also failed to find relevant examples.

Any ideas?

Answer

Here is a simple example showing how to properly set edge attributes and how to generate a weighted incidence matrix.

import networkx as nx
from math import sqrt

G = nx.grid_2d_graph(3,3)
for s, t in G.edges():
    x1, y1 = s
    x2, y2 = t
    G[s][t]['weight']=sqrt((x2-x1)**2 + (y2-y1)**2)*42

print(nx.incidence_matrix(G,weight='weight').todense())

OUTPUT

[[ 42.  42.  42.   0.   0.   0.   0.   0.   0.   0.   0.   0.]
 [  0.   0.   0.  42.  42.  42.   0.   0.   0.   0.   0.   0.]
 [ 42.   0.   0.   0.   0.   0.  42.   0.   0.   0.   0.   0.]
 [  0.   0.   0.   0.   0.   0.   0.  42.  42.  42.   0.   0.]
 [  0.  42.   0.  42.   0.   0.   0.   0.  42.   0.  42.   0.]
 [  0.   0.   0.   0.   0.   0.   0.  42.   0.   0.   0.  42.]
 [  0.   0.   0.   0.   0.  42.   0.   0.   0.  42.   0.   0.]
 [  0.   0.   0.   0.   0.   0.  42.   0.   0.   0.  42.  42.]
 [  0.   0.  42.   0.  42.   0.   0.   0.   0.   0.   0.   0.]]

If you want a particular ordering of the nodes and edges in the matrix use the nodelist= and edgelist= optional parameters to networkx.indicence_matrix().