Constructed example with some explanations (provided by Ludo Waltman)The next constructed network was provided by Ludo Waltman (AppendixB.net).
For details see AppendixB of the paper:
Ludo Waltman, Nees Jan van Eck, and Ed C.M. Noyons (2010): A unified approach to mapping and clustering of bibliometric networks. Journal of Informetrics, 4, 629-635
Network has 31 vertices and 155 lines. There are different line values (see picture bellow):
Resolution parameter r=1For resolution parameter r=1 Louvain method and VOS Clustering find almost the same partitions into 3 clusters. The difference is in position of vertex 31 (belonging to 'green' cluster in Louvain and 'yellow' cluster in the VOS partition). Visually both partitions seems equally good, but looking at Q and VOSQ values there are small differences that make one partition a bit better than the other.
Detailed explanation why this happen and why the partition obtained by VOS might be a better one can be found in AppendixB of the paper: