Real example: Slovenian municipalities
Download Slovenian municipalities network (210 counties, 549 edges). Since some special Slovenian letters (č, š, and ž) are used in names of municipalities NET file is saved as Unicode UTF8 file with BOM, which can be read by Pajek.Two municipalities are connected by an edge if they are geographical neighbours. Edge value represents similarity (computed from some statistical variables) among two municipalities. Vertices representing municipalities have real - geograpical - coordinates. Partition to communities in this case gives regionalization of municipalities.
For resolution r=1 we get the following correlations among partitions obtained by Louvain method and VOS Clustering (Louvain method finds partition into 10 clusters, VOS Clustering into 13 clusters):
Cramers V: 0.76811012
Rajski(C1 <-> C2): 0.55834039
Rajski(C1 -> C2): 0.76974462
Rajski(C1 <- C2): 0.67029072
Adjusted Rand Index: 0.48208922
| Best partition according to Louvain method Q(r=1)=0.759173, 10 clusters, SVG | Best partition according to VOS Clustering VOSQ(r=1)=0.8179118, 13 clusters, SVG |
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Regionalization to 3 regions can be obtained by setting r=0.1. Both solutions are very similar also according to correlations:
Cramer's V: 0.88523985
Rajski(C1 <-> C2): 0.63564555
Rajski(C1 -> C2): 0.78578494
Rajski(C1 <- C2): 0.76888124
Adjusted Rand Index: 0.74963115
| Best partition according to Louvain method Q(r=0.1)=0.929470, 3 clusters, SVG | Best partition according to VOS Clustering VOSQ(r=0.1)=0.941877, 3 clusters, SVG |
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Comparing Louvain method and VOS Clustering Back to Pajek and Pajek-XXL Main page.