Multilevel Graph Clustering with Density-Based Quality Measures

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A The Benchmark Graph Collectionsubset vertices edges mean wdeg wgt. density sourceSciMet main S 2678 10369 7.75541 4.8151e-05 pajek-citationODLIS main S 2898 16381 12.70842 2.7156e-05 pajek-lingDutchElite main 3621 4310 2.38111 0.00011598 pajek-socialgeom main 3621 9461 10.91964 2.5291e-05 pajek-citationEpa main R S 4253 8897 4.21020 5.5847e-05 pajek-webeva main 4475 4654 2.08402 0.00010725 pajek-econUSpowerGrid R 4941 6594 5.33819 3.7913e-05 pajek-mixedhep-th main S 5835 13815 4.68711 3.6564e-05 Newman-coauthErdos02 S C 6927 11850 3.42139 4.2194e-05 pajek-socialLederberg main R S 8212 41436 10.10801 1.2048e-05 pajek-citationPairsP R S 10617 63786 115.39098 8.1627e-07 pajek-lingPGPgiantcompo S 10680 24316 4.55805 2.0542e-05 Arenas-socialastro-ph main R S 14845 119652 4.49610 1.4982e-05 Newman-coautheatRS S 23219 305501 67.90641 6.3464e-07 pajek-lingDIC28 main R S C 24831 71014 5.71979 7.0409e-06 pajek-linghep-th-new main S 27400 352059 25.73161 1.4184e-06 pajek-citationcond-mat-2003 main S 27519 116181 4.41826 8.2246e-06 Newman-coauthTable A.2: References to the Graph SourcesANoack-generatedpajek-citationpajek-socialNewman-lingNewmanNewman-coauthpajek-bioArenas-bioNewman-bioUriAlonpajek-lingArenaspajek-webpajek-econANoackpajekRRottaanoackNotreDame-bioArenas-socialpajek-mixedweb addresshttp://www-sst.informatik.tu-cottbus.de/~an/GD/http://vlado.fmf.uni-lj.si/pub/networks/data/http://vlado.fmf.uni-lj.si/pub/networks/data/http://www-personal.umich.edu/~mejn/netdata/http://www-personal.umich.edu/~mejn/netdata/http://www-personal.umich.edu/~mejn/netdata/http://vlado.fmf.uni-lj.si/pub/networks/data/bio/foodweb/foodweb.htmhttp://deim.urv.cat/~aarenas/data/welcome.htmhttp://www-personal.umich.edu/~mejn/netdata/http://www.weizmann.ac.il/mcb/UriAlon/http://vlado.fmf.uni-lj.si/pub/networks/data/http://deim.urv.cat/~aarenas/data/welcome.htmhttp://vlado.fmf.uni-lj.si/pub/networks/data/mix/mixed.htmhttp://vlado.fmf.uni-lj.si/pub/networks/data/econ/Eva/Eva.htmhttp://www-sst.informatik.tu-cottbus.de/~an/GD/http://vlado.fmf.uni-lj.si/pub/networks/data/sport/football.htmhttp://goya.informatik.tu-cottbus.de/~clustering/http://www.informatik.tu-cottbus.de/~an/GD/http://vlado.fmf.uni-lj.si/pub/networks/data/ND/NDnets.htmhttp://deim.urv.cat/~aarenas/data/welcome.htmhttp://vlado.fmf.uni-lj.si/pub/networks/data/mix/mixed.htm100
B Clustering ResultsTable B.1: Random Walk Distance by Graph1 2 3 4 5 WD-sgrdSouthernWomen 0.33449 0.31530 0.31530 0.33184 0.33449 0.31972dolphins 0.46220 0.52680 0.46642 0.46642 0.46642 0.52587prison alon 0.56098 0.61317 0.61739 0.61667 0.60873 0.62077polBooks 0.52694 0.52694 0.52694 0.52694 0.52694 0.52724adjnoun 0.24411 0.27143 0.30637 0.28173 0.26923 0.31078jazz 0.44403 0.44403 0.44424 0.44403 0.44447 0.44468sandi main 0.70997 0.80704 0.80215 0.81677 0.80646 0.82773celegansneural 0.48148 0.47932 0.47936 0.48499 0.50224 0.50295USAir97 0.35050 0.35093 0.35246 0.35804 0.36082 0.36824celegans metabolic 0.42627 0.43558 0.42427 0.42970 0.43405 0.45070circuit s838 0.67174 0.81058 0.76911 0.77549 0.80461 0.81551polBlogs main 0.43162 0.43219 0.43219 0.43219 0.43219 0.43237Yeast main 0.54016 0.57924 0.58575 0.59310 0.58996 0.62179Epa main 0.58271 0.63287 0.63498 0.63672 0.64941 0.66843USpowerGrid 0.84679 0.90077 0.86988 0.90234 0.87756 0.93795Lederberg main 0.61540 0.64291 0.66511 0.66392 0.68129 0.70339PairsP 0.50587 0.58476 0.58308 0.58951 0.58975 0.65067astro-ph main 0.65154 0.71070 0.70995 0.71056 0.71071 0.76261DIC28 main 0.72153 0.77391 0.77093 0.77864 0.78366 0.84747Table B.2: Random Walk Reachability, Length 2RWreach-sgrd 1 RWreach-sgrd 3 RWreach-sgrd 5 WD-sgrdSouthernWomen 0.31972 0.31972 0.33449 0.31972dolphins 0.52852 0.52852 0.52852 0.52587prison alon 0.62077 0.61464 0.61288 0.62077polBooks 0.52724 0.52724 0.52724 0.52724adjnoun 0.30194 0.30359 0.30750 0.31078jazz 0.44487 0.44452 0.44487 0.44468sandi main 0.82760 0.82779 0.82779 0.82773celegansneural 0.50295 0.50382 0.50353 0.50295USAir97 0.36824 0.36603 0.36824 0.36824celegans metabolic 0.44966 0.44989 0.44182 0.45070circuit s838 0.80524 0.81521 0.81551 0.81551polBlogs main 0.43237 0.43228 0.43228 0.43237Yeast main 0.62207 0.62328 0.62593 0.62179Epa main 0.66783 0.66795 0.66568 0.66843USpowerGrid 0.93717 0.93882 0.93919 0.93795Lederberg main 0.70267 0.70323 0.70402 0.70339PairsP 0.65476 0.65361 0.65386 0.65067astro-ph main 0.76248 0.76329 0.76409 0.76261DIC28 main 0.85097 0.85162 0.85158 0.84747Table B.3: Random Walk Reachability, Length 3RWreach-sgrd 1 RWreach-sgrd 3 RWreach-sgrd 5 WD-sgrdSouthernWomen 0.31972 0.32635 0.33184 0.31972dolphins 0.52852 0.52680 0.52680 0.52587101
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Brandenburgische Technische Univers
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ContentsList of FiguresList of Tabl
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List of Figures1.1 Graph of the Mex
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1 IntroductionSince the rise of com
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1.2 Objectives and Outline1.2 Objec
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2 Graph ClusteringThis chapter intr
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2.2 The Modularity Measure of Newma
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2.3 Density-Based Clustering Qualit
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2.4 Fundamental Clustering Strategi
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3 The Multi-Level Refinement Algori
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3.1 The Multi-Level Schemeas starti
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3.2 Graph CoarseningData: graph,sel
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3.2 Graph Coarseningnearly no edges
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3.3 Merge SelectorsExtent Name Desc
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3.3 Merge Selectorsdifferent size.
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3.3 Merge SelectorsThe probability
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3.3 Merge SelectorsAs selection qua
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3.3 Merge Selectorsvectors the eige
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3.4 Cluster Refinementleave the loc
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3.4 Cluster Refinementmoving v from
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3.4 Cluster RefinementAlgorithm Sea
Page 59 and 60: 3.4 Cluster RefinementData: graph,c
Page 61 and 62: 3.4 Cluster RefinementModularity0.2
Page 63 and 64: 3.5 Further Implementation NotesInd
Page 65 and 66: 3.5 Further Implementation NotesBOO
Page 67: 3.5 Further Implementation Notesfor
Page 70 and 71: 4 Evaluationparameter component des
Page 72 and 73: 4 Evaluationsignificance scale also
Page 74 and 75: 4 EvaluationModularity by Match Fra
Page 76 and 77: 4 Evaluation5% 10% 30% 50% 100%G-no
Page 78 and 79: 4 Evaluationmean modularity0.50 0.5
Page 80 and 81: 4 Evaluation1 2 3 4RWreach-none 1 0
Page 82 and 83: 4 EvaluationG-none M-none G-sgrd M-
Page 84 and 85: 4 Evaluationmean modularity time DI
Page 86 and 87: 4 EvaluationRuntime vs. Graph SizeR
Page 88 and 89: 4 EvaluationComparison of Modularit
Page 90 and 91: 4 Evaluation(a) karate(b) dolphinsF
Page 92 and 93: 4 Evaluation(a) jazz(b) celegans me
Page 94 and 95: 4 Evaluationadministrators, and gra
Page 97 and 98: 5 Results and Future WorkThe object
Page 99 and 100: 5.3 Directions for Future Workstrat
Page 101: 5.3 Directions for Future Workties
Page 104 and 105: BIBLIOGRAPHY[14] B.L. Chamberlain.
Page 106 and 107: BIBLIOGRAPHY[42] H. Jeong, B. Tombo
Page 108 and 109: BIBLIOGRAPHY[71] A. J. Soper and C.
Page 112 and 113: B Clustering ResultsRWreach-sgrd 1
Page 114: B Clustering Resultswalktrap leadin
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Multilevel Graph Clustering with Density-Based Quality Measures

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