Multilevel Graph Clustering with Density-Based Quality Measures

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BIBLIOGRAPHY[71] A. J. Soper and C. Walshaw. A generational scheme for partitioning graphs.In L. Spector et al., editor, Proc. Genetic & Evolutionary Comput. Conf.(GECCO-2001), pages 607–614. Morgan Kaufmann, San Francisco, 2001.[72] A. J. Soper, C. Walshaw, and M. Cross. A combined evolutionary search andmultilevel approach to graph partitioning. In D. Whitley et al., editor, Proc.Genetic & Evolutionary Comput. Conf. (GECCO-2000), pages 674–681. MorganKaufmann, San Francisco, 2000.[73] A. J. Soper, C. Walshaw, and M. Cross. A combined evolutionary search andmultilevel optimisation approach to graph partitioning. Tech. Rep. 00/IM/58,Comp. Math. Sci., Univ. Greenwich, London SE10 9LS, UK, April 2000.[74] A. J. Soper, C. Walshaw, and M. Cross. A combined evolutionary search andmultilevel optimisation approach to graph partitioning. J. Global Optimization,29(2):225–241, 2004.[75] Stijn van Dongen. Graph Clustering by Flow Simulation. PhD thesis, Universityof Utrecht, May 2000.[76] Ken Wakita and Toshiyuki Tsurumi. Finding community structure in megascalesocial networks. cs/0702048, February 2007.[77] David Wales and Jonathan Doye. Global optimization by basin-hopping and thelowest energy structures of lennard-jones clusters containing up to 110 atoms.cond-mat/9803344, March 1998. J. Phys. Chem. A 101, 5111-5116 (1997).[78] C. Walshaw and M. Cross. Mesh partitioning: a multilevel balancing andrefinement algorithm. SIAM J. Sci. Comput., 22(1):63–80, 2000.[79] J.H. Ward Jr. Hierarchical grouping to optimize an objective function. Journalof the American Statistical Association, 58(301):236–244, 1963.[80] Scott White and Padhraic Smyth. A spectral clustering approach to findingcommunities in graph. SIAM Data Mining Conference, 2005.[81] Wu and Huberman. Finding communities in linear time: a physics approach.The European Physical Journal B - Condensed Matter and Complex Systems,38:331–338, March 2004.[82] W. W. Zachary. An information flow model for conflict and fission in smallgroups. Journal of Anthropological Research, 33:452–473, 1977.[83] Zhou and Lipowsky. Network brownian motion: A new method to measurevertex-vertex proximity and to identify communities and subcommunities.Computational Science - ICCS 2004, 2004.98
A The Benchmark Graph CollectionThe Table A.1 contains a list of the used benchmarks graphs. The graphs are sortedby their number of vertices. For each graph the number of vertices and edges, theweighted mean vertex degree (mean wdeg) and the global connection density in thedegree volume model (wgt. density) is printed. Graphs with the suffix main arejust the largest connectivity component of the original graph. The second columnmarks the graphs used in the reduced set (R), in the scalability analysis (S), andin the comparison to reference algorithms (C ). The last column gives a short sourcereference. Links to the corresponding websites can be found in Table A.2.Table A.1: The Benchmark Graph Collectionsubset vertices edges mean wdeg wgt. density sourceChain8 S C 8 7 1.75000 0.071429 ANoack-generatedStar9 C 9 8 1.77778 0.06250 ANoack-generatedK55 S C 10 25 5.00000 0.02000 RRottaStudent government 11 32 7.45455 0.012195 pajek-socialTree15 C 15 14 1.86667 0.035714 ANoack-generatedModMath main C 30 61 4.06667 0.0081967 pajek-socialSouthernWomen R C 32 89 5.56250 0.005618 pajek-socialHi-tech main S 33 91 8.90909 0.0034014 pajek-socialkarate C 34 78 4.58824 0.0064103 Newmanfootball 35 118 16.85714 0.0016949 pajekmexican power C 35 117 6.68571 0.0042735 pajekGrid66 C 36 60 3.33333 0.0083333 ANoack-generatedmorse 36 666 1324.38889 2.2390e-05 anoackSawmill C 36 62 3.44444 0.0080645 pajek-socialFood 45 990 507.82222 4.376e-05 ANoackdolphins R C 62 159 5.12903 0.0031447 pajek-socialWorldImport1999 66 2145 132361.51897 1.1447e-07 ANoackprison alon R 67 142 5.43284 0.0027473 UriAlonlesmis S 77 254 21.29870 0.00060976 Newmanworld trade 80 875 1644039.85000 7.6032e-09 pajek-econpolBooks R C 105 441 8.40000 0.0011338 pajek-mixedadjnoun R C 112 425 7.58929 0.0011765 Newman-lingafootball 115 613 10.71304 0.00081169 Newmanbaywet 128 2075 54.05277 0.00014453 pajek-biojazz R 198 2742 55.39394 9.1174e-05 ArenasA99m main S 233 325 2.79828 0.0015337 pajek-socialSmallW main S 233 994 17.06438 0.00025151 pajek-citationA01 main S 249 635 5.15663 0.00077882 pajek-citationsandi main R C 253 307 2.42688 0.0016287 pajek-citationcelegansneural R S 297 2148 59.37374 5.6709e-05 Newman-bioUSAir97 R C 332 2126 12.80723 0.00023518 pajek8Clusters 400 24063 238.63000 1.0476e-05 ANoack-generatedWorldCities main 413 7518 81.80145 2.96e-05 pajek-mixedcelegans metabolic R 453 2040 20.24283 0.00010931 Arenas-biocircuit s838 R C 512 819 3.19922 0.0006105 UriAlonRoget main S 994 3641 10.17807 9.8853e-05 pajek-lingCSphd main S C 1025 1043 2.03512 0.00047939 pajek-socialemail 1133 5451 19.24448 4.5863e-05 ArenaspolBlogs main R 1222 16717 31.23977 2.6197e-05 pajek-mixedNDyeast main S 1458 1993 2.70302 0.00025664 NotreDame-bioYeast main R 2224 7049 6.14119 7.5576e-05 pajek-bio99
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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
Page 57 and 58: 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 110 and 111: A The Benchmark Graph Collectionsub
Page 112 and 113: B Clustering ResultsRWreach-sgrd 1
Page 114: B Clustering Resultswalktrap leadin
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