Counting multiple edges in graph (python)

Question

I am generating a network of size N with a power-law degree distribution using the so-called configuration_model algorithm. The resulting graph allows multiple edges, I have to count them but I cannot figure out how. Here is a possible solution:

import networkx as nx
import numpy as np
from networkx.utils import (powerlaw_sequence, create_degree_sequence)

deg_sequence = create_degree_sequence(num, powerlaw_sequence, exponent=2.2)
graph=nx.configuration_model(deg_sequence)

num_par = sum(len(graph[node][neigh]) for node in graph for neigh in graph.neighbors_iter(node)) // 2
print ('Graph has %d multi-links' %num_par)

self_loops=len(graph.selfloop_edges())
print ('Graph has %d self-loops' %self_loops)

edges=len(graph.edges())
print edges

I borrowed the sixth line of code somewhere on the internet but frankly I can't quite understand how it works. In particular I can't understand what is (graph[node][neigh]) of which it calculates the length. To me, it does not seem like a list either, but I am sure it's me not getting the idea here. Btw as a result of this code I get a very high percentage of multiple edges, more than 98% of the total number of links, and it does not seem very good to me. Is this way of calculating parallel edges correct? If so, would you explain me how it works? Do you know any other way of doing it?

What value does num have?

Paul Brodersen
– Paul Brodersen

2017-03-28 10:16:56 +00:00
Commented Mar 28, 2017 at 10:16 — Paul Brodersen
– Paul Brodersen, Commented Mar 28, 2017 at 10:16

Paul Brodersen · Accepted Answer · 2017-03-28 10:42:44Z

3

If you write out line 6 in for-loops instead of list expressions, you arrive at the following:

num_par = 0
for node in graph:
    for neigh in graph.neighbors(node):
        num_par += len(graph[node][neigh]) / 2.

I am not sure what that line is counting; I am sure that it is not calculating the number of multi-edges correctly.

If you just plot the graph as an array (num = 100), you can immediately see that there are very few multi-edges:

arr = nx.to_numpy_matrix(graph)
plt.imshow(arr, interpolation='nearest', cmap='gray'); plt.show()

The number of multi-edges is easily calculated with

num_multiedges = np.sum(arr>=2) / 2 # divide by two as graph is undirected

answered Mar 28, 2017 at 10:42

Paul Brodersen

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2 Comments

sato Over a year ago

Thank you Paul, I am still familiarizing with numpy, this is exactly what I needed! BTW I re-wrote that list comprehension like you did and I too could not figure out what it was doing, that's why I asked. The author claimed it was a multi edge counter, I wasn't sure it was either me not understanding or the code that was wrong. Again, thanks a lot.

VMAtm Over a year ago

Ahh, beaten me in couple of hours. Nice answer!

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