Discrepancy in Assortativity Coefficient Values between Networkit and Networkx

[Fabio-Giacomelli]

Hello,

I've encountered an issue with the Assortativity class in Networkit. When comparing the assortativity coefficient calculated by Networkit and Networkx for the same graph, I noticed a discrepancy in the values.

Here's the code snippet I used for testing:

import networkx as nx 
import networkit as nk
from networkit.correlation import Assortativity
from networkit.generators import BarabasiAlbertGenerator
from networkit.centrality import DegreeCentrality

generator = BarabasiAlbertGenerator(1, 100)
nkG = generator.generate()
r_nk = Assortativity(nkG, DegreeCentrality(nkG).run().scores()).run().getCoefficient()
nxG = nk.nxadapter.nk2nx(nkG)
r_nx = nx.degree_assortativity_coefficient(nxG)

print(r_nk, r_nx)

The assortativity coefficient computed with Networkit returns positive values, while the one computed with Networkx returns negative values. I believe the usage of the Assortativity class is correct, or am I wrong?

Could you please look into this issue? Any guidance or clarification would be greatly appreciated.

Thank you, Fabio

[fabratu]

Hi Fabio,

thanks for bringing this up. Your code does correctly use Assortativity from NetworKit and NetworkX. Our documentation is a bit imprecise, since it computes something related to what NetworkX is doing - but not the same thing.

Our function computes a sample pearson correlation coefficient, which is for example described here: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient#For_a_sample

In NetworkX, the standard pearson correlation coefficient (scalar mixing) is computed. Information about the formula can be seen here: https://journals.aps.org/pre/pdf/10.1103/PhysRevE.67.026126 (formula [21])

While both numbers are between -1 and 1, the difference is, that the sample approach considers (only) the correlation between numbers. If we relate this to degrees, a node with a higher degree should therefore connect to another node with a higher degree. The standard pearson correlation coefficient considers the mixing of the degree of both endpoints. That means, that the difference between degrees should also be minimized.