Multilevel Graph Clustering with Density-Based Quality Measures

4 Evaluation(a) jazz(b) celegans metabolicFigure 4.13: Reference Graphs (polBooks and celegans metabolic)average seven intra- and four inter-conference games are played and inter-conferencegames between geographical close teams are more likely. A picture of the graph isvisible in Figure 4.12b.Newman’s greedy joining algorithm found 6 clusters with modularity 0.546 [60]whereas the spectral methods of White et al. found 11 clusters with 0.602 [80].Similarly the random walk based agglomeration of Pons found modularity 0.60 [64].With Fractional Linear Programming and rounding a clustering of 0.6046 and theupper bound 0.606 was found [2]. The random walk based multi-level clusteringML-KL-rw comes close to this bound with 10 clusters and modularity 0.60582. Thesimpler variant ML-KL-density just got modularity 0.59419 with 7 clusters.jazz A network of 198 Jazz musicians compiled by Geisler and Danon [33]. Suchgraphs are interesting for the social sciences as Jazz musicians very often worktogether in many different small groups (Fig. 4.13a). This graph also became verypopular for the comparison of clustering methods.A picture of the graph is shown on the right.The best clustering was reported for Extremal Optimization with 5 clusters ofmodularity 0.4452 [23]. Fractional Linear programming with rounding gave modularity0.445 [2] and an upper bound of 0.446. Spectral clustering methods yieldedmodularity 0.437 [21], 0.444 [20], and 0.442 [58]. The worst modularity 0.4409 [17]was produced by Danon’s greedy joining with modified merge selector. Both multilevelalgorithms found 4 clusters with modularity 0.44514 (ML-KL-rw) and 0.44487(ML-KL-density).82