Multilevel Graph Clustering with Density-Based Quality Measures

4.7 Comparison to Published Results(a) circuit s838(b) emailFigure 4.14: Reference Graphs (circuit s838 and email)celegans metabolic A metabolic network for the nematode Caenorhabditis elegans[42, 23]. The graph describes chemical reactions as well as the regulatoryinteractions that guide these reactions (Fig. 4.13b).The first published clustering result of this graph was found by Extremal Optimizationwith 12 clusters of modularity 0.4342 [23]. Greedy joining with precoarseningby short random walks found 7 clusters with modularity 0.4164 [65].Newman’s recursive spectral bisection yielded 0.435 [58]. The recursive bisection algorithmwith Quadratic Programming of Agarwal and Kempe found the to date bestpublished clustering with modularity 0.450. The two multi-level refinement algorithmsgave similar results with 0.44992 (ML-KL-rw) and 0.45090 (ML-KL-density).The best clustering with experimental configurations had modularity 0.45136.circuit s838 The electric circuit s838 st.txt of Uri Alon’s collection of complexnetworks [53]. This graph is an undirected version with 512 vertices connected by819 edges (Fig. 4.14a).The only published clustering has modularity 0.815 with 13 clusters [69]. Bothmulti-level configurations found clusterings of similar modularity. The random walkbased greedy grouping ML-KL-rw is with 0.815507 slightly worse than ML-KLdensitywith the weight density selector which got 0.815513. However better clusteringsexist. For example with experimental configurations a clustering with 12clusters and modularity 0.81719 was found.email The network of e-mail interchanges between members of the UniversityRovira i Virgili in Tarragona, Spain [36, 37]. The graph contains 1133 users ofthe university e-mail system, including faculty, researchers, technicians, managers,83