Effect of edge weights in resulting communities

[paula-tataru]

Hi,

Thank you for developing this nice library! I have been trying to understand how weights affect the resulting detected communities and I found something which I did not expect.

Using the example graph you provided in the readme file, I created two versions containing weights on the edges - the edge weights in one version are scaled by a constant relative to the other version:

v1:

0	1	1
1	2	1
2	0	1
2	3	0.5
3	5	1
5	4	1
4	3	1

v2:

0	1	4
1	2	4
2	0	4
2	3	2
3	5	4
5	4	4
4	3	4

I ran the Leiden algorithm using the following options java -cp networkanalysis-1.1.0.jar nl.cwts.networkanalysis.run.RunNetworkClustering -r 0.2 -w

For v1, the same communities are detected as for the example in the readme file:

0	0
1	0
2	0
3	1
4	1
5	1

For v2, all nodes are part of one community:

0	0
1	0
2	0
3	0
4	0
5	0

I found this a bit surprising, as I didn't expect the scale of the weights to be so important and I expected to obtain the same results for these two networks.

I can see that in v1.1 of the library, two normalization methods have been introduced for the edge weights, but I couldn't find an explanation for why / when this might be needed and how the different normalization methods might impact the result.

Would it be possible to provide a brief explanation for this?

Thank you.

Best, Paula Tataru