Managing and mining graph data

621 Pages·2010·95.87 MB·English

by  Charu C. Aggarwal

Managing and Mining Graph Data

by

Charu C. Aggarwal
IBM T.J. Watson Research Center
Hawthorne, NY, USA

Haixun Wang
Microsoft Research Asia
Beijing, China
Charu C. Aggarwal Haixun Wang
IBM Microsoft Research Asia
Thomas J. Watson Research 49 Zhichun Road
Center 100190 Beijing
19 Skyline Drive 5F Sigma Center

Hawthorne, NY10532 China, People’s Republic

USA [email protected]
[email protected]
ISSN 1386-2944
ISBN 978-1-4419-6044-3 e-ISBN 978-1-4419-6045-0

DOI10.1007/978-1-4419-6045-0
Sprin ger New York Dordrecht Heidelberg London

L ibrary of Congress Control Number: 2010920842

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Contents
tLsiofgiFures xv
tLsiofabelsT xxi
arcPeef xxiii
1
AnInrtoducoitnotGraphDaat 1
CharuC.AggarwalandHaixunWang
1. Inrtoducoitn 1
2. GraphManagementandMninigAppcilaoitns 3
3. uSmmary 8
efRerences 9
2
GraphDaatManagementandMninig:AyuServofAglorhtimsandAppcilaoitns 13
CharuC.AggarwalandHaixunWang
1. Inrtoducoitn 13
2. GraphDaatManagementAglorhtims 16
2.1 InxdniegandQueryrPoniscgesechnqiuesT 16
2.2 eacRhabytiliQuereis 19
2.3 GraphMacthnig 21
2.4 oyrdweKeSarch 24
2.5 ySnopsisoCnrtuscoitnofeviMsasGraphs 27
3. GraphMninigAglorhtims 29
3.1 aettrnPMninigniGraphs 29
3.2 uletrCsnigAglorhtimsforGraphDaat 32
3.3 cfiaoiitsnalsCAglorhtimsforGraphDaat 37
3.4 TheDynamcisofomivlen-iEgvTGraphs 40
4. GraphAppcilaoitns 43
4.1 hCemcialandoioBlgcialAppcilaoitns 43
4.2 ebWAppcilaoitns 45
4.3 aorSefwtuBgLocazilaoitn 51
5. oCnculoisnsanduFutreeaersRch 55
efRerences 55
3
GraphMninig:wsLaandGeneraotrs 69
DeepayanChakrabarti, ChristosFaloutsosandMaryMcGlohon
1. Inrtoducoitn 70
2. GraphaettrnsP 71
vi
MANAGINGANDMININGGRAPHDATA
2.1 weroPwsLaandaelidvy-THeauoitnrtsbiDsi 72
2.2 mSallDaimeetrs 77
2.3 OhteractitSGraphaettrnsP 79
2.4 aettrnsPniovlniEgvGraphs 82
2.5 ThertSucutreofpSeccfiiGraphs 84
3. GraphGeneraotrs 86
3.1 anRdomGraphModesl 88
3.2 rPeferenaitlaAttchmentandarainstV 92
3.3 Opmitziaoitn-beadsgeneraotrs 101
3.4 -beeadnsosrT 108
3.5 Generaotrsforpseccfiigraphs 113
3.6 GraphGeneraotr:sAusmmary 115
4. oCnculoisns 115
efRerences 117
4
QueryLanguageandAccsesMehtodsforGraphDaatbeass 125
HuahaiHeandAmbujK.Singh
1. Inrtoducoitn 126
1.1 Graph-sa-ta-miteQuereis 126
1.2 GraphpSeccfiiOpmitziaoitns 127
1.3 GraphQL 128
2. OperaoitnsonGraphrtSucutres 129
2.1 oCncaetnaoitn 130
2.2 ujDsincoitn 131
2.3 epRoietitn 131
3. GraphQueryLanguage 132
3.1 DaatModel 132
3.2 GraphaettrnsP 133
3.3 GraphAglebra 134
3.4 RWLFExpoirsness 137
3.5 evExpirsesweroP 138
4. ImpelmenaotitnofhteeeSlcoitnOperaotr 140
4.1 GraphaettrnPMacthnig 140
4.2 LocalrPunnigandalverteRiofbieFaselMaets 142
4.3 oJnitedRucoitnofeSarchpSace 144
4.4 OpmitziaoitnofeSarchOrder 146
5. ExpermienatlutSdy 148
5.1 oioBlgcialorNekwt 148
5.2 ySnhtecitGraphs 150
6. ealetdRorkW 152
6.1 GraphQueryLanguages 152
6.2 GraphInxdnieg 155
7. uFutreeaesrRchDriecoitns 155
8. oCnculoisn 156
Appendxi:QueryySnatxofGraphQL 156
efRerences 157
5
GraphInxdnieg 161
XifengYanandJiaweiHan
1. Inrtoducoitn 161
vii
Contents
2. eFautreead-sBGraphInxde 162
2.1 ahtsP 163
2.2 rFequentrtSucutres 164
2.3 evcrDsiminiaitrtSucutres 166
2.4 oledCsrFequentrtSucutres 167
2.5 reesT 167
2.6 HeirarchcialInxdnieg 168
3. rtSucutremiSalirytieSarch 169
3.1 eFautreead-sBrtSucutraletlriFnig 170
3.2 eFautresMsimitEaositn 171
3.3 rFequyencferencDfei 172
3.4 eFautreeSteeSlcoitn 173
3.5 rtSucutreshwtiGaps 174
4. erevseRuSbrtuscutreeSarch 175
5. oCnculoisns 177
efRerences 178
6
GrapheacRhabytiliQuer:eisAyuServ 181
JeffreyXuYuandJiefengCheng
1. Inrtoducoitn 181
2. eralvsraTApproaches 186
2.1 reIeP+SST 187
2.2 IPGPR 187
3. Dua-lLabenilg 188
4. reeTervoC 190
5. hCaniervoC 191
5.1 oCmpunitghteOpmitalhCaniervoC 193
6. reeaht-TPervoC 194
7. 2-HOPervoC 196
7.1 AHeucitrsianRknig 197
7.2 AGeomertceiaad-lsBApproach 198
7.3 GrapharoititnnPigApproaches 199
7.4 2-HopervoCManietnance 202
8. 3-HopervoC 204
9. arewatnDsice-A2-HopervoC 205
10. GraphaettrnPMacthnig 207
10.1 ApSecailea:sC 𝐴, 𝐷 208
10.2 TheGeneraleassC → 211
11. oCnculoisnsanduSmmary 212
efRerences 212
7
ExactandIxnacetGraphMacthnig:MehtodoolgyandApopicinlats 217
KasparRiesen, XiaoyiJiangandHorstBunke
1. Inrtoducoitn 218
2. ciasBNoaotitns 219
3. ExactGraphMacthnig 221
4. IxnacetGraphMacthnig 226
4.1 GraphEdtiatnDsice 227
4.2 OhterIxnacetGraphMacthnigechnqiuesT 229
5. GraphMacthnigforDaatMninigandInformaoitnalverteRi 231
ivii
MANAGINGANDMININGGRAPHDATA
6. ecotrVpSaceEmbeddnigsofGraphsvaiGraphMacthnig 235
7. oCnculoisns 239
efRerences 240
8
AyuServofAglorhtimsforoyrdweKeSarchonGraphDaat 249
HaixunWangandCharuC.Aggarwal
1. Inrtoducoitn 250
2. oyrdweKeSarchonXMLDaat 252
2.1 QueryeSmancits 253
2.2 AnwersanRknig 254
2.3 AglorhtimsforA-LCbeadsoyrdweKeSarch 258
3. oyrdweKeSarchoneaolitRnalDaat 260
3.1 QueryeSmancits 260
3.2 XpDBolrerandVERODICS 261
4. oyrdweKeSarchoncShema-rFeeGraphs 263
4.1 QueryeSmancitsandAnwersanRknig 263
4.2 GraphExpolraoitnbyaarckdBweSarch 265
4.3 GraphExpolraoitnbydirBiecoitnaleSarch 266
4.4 Inxd-ebeadsGraphExpolraoitn–hteLIBNKSAglorhtim 267
4.5 TheObanejcRtkAglorhtim 269
5. oCnculoisnsanduFutreeaersRch 271
efRerences 271
9
AyuServofuletrCsnigAglorhtimsforGraphDaat 275
CharuC.AggarwalandHaixunWang
1. Inrtoducoitn 275
2. NodeuletrCsnigAglorhtims 277
2.1 TheMnimiumuCtrPobelm 277
2.2 aMyu-itlwGrapharoititnnPig 281
2.3 envoitnaloCnGenerazilaoitnsandorNekwtrtSucutreIndcies
282
2.4 Thewmanan-NeGrivAglorhtim 284
2.5 ThepSecrtaluletrCsnigMehtod 285
2.6 DeetrmninigQuqil-iauCses 288
2.7 TheeasCofevisMasGraphs 289
3. uletrCsnigGraphsasObejcst 291
3.1 ExetndnigcialsalsCAglorhtimsotrtSucutralDaat 291
3.2 TherXPojApproach 293
4. AppcilaoitnsofGraphuletrCsnigAglorhtims 295
4.1 oCmmunytiDeetcoitnniebWAppcilaoitnsandoScailNe-t
orkws 296
4.2 eelcommunciaoitnTorNekwts 297
4.3 EmaliAnaylsis 297
5. oCnculoisnsanduFutreeaersRch 297
efRerences 299
10
AyuServofAglorhtimsforDenesuSbgraphervycoDsi 303
VictorE.Lee, NingRuan, RuomingJinandCharuAggarwal
1. Inrtoducoitn 304
xi
Contents
2. ypesTofDenesoCmponenst 305
2.1 Abosuletv.sevealitRDenytis 305
2.2 GraphermnioolgyT 306
2.3 DenfioitinsofDenesoCmponenst 307
2.4 DenesoCmponenteeSlcoitn 308
2.5 eaolitRnhspibewteenuletrCssandDenesoCmponenst 309
3. AglorhtimsforDeetcnitgDenesoCmponenstnianiSgelGrpah 311
3.1 ExactEnumeraoitnApproach 311
3.2 HeucitrsiApproach 314
3.3 ExactandApproxmiaoitnAglorhtimsforernvicgoDsiDe-ns
tesoCmponenst 322
4. rFequentDenesoCmponenst 327
4.1 rFequentaettrnsPhwtiDenytisoCnrtasnist 327
4.2 DenesoCmponensthwtirFequyencoCnrtasnit 328
4.3 Enumeranitgr-oCsGrsaphQuqil-iauCses 328
5. AppcilaoitnsofDenesoCmponentAnaylsis 329
6. oCnculoisnsanduFutreeaersRch 331
efRerences 333
11
GraphcfiaoiitsnalsC 337
KojiTsudaandHirotoSaigo
1. Inrtoducoitn 337
2. GrapherneslK 340
2.1 anRdomaklsWonGraphs 341
2.2 LabeleSquenceernelK 342
2.3 cefiintEfoCmpuaotitnofLabeleSquenceerneslK 343
2.4 Exetnoisns 349
3. GraphoBonitsg 349
3.1 ormFuaolitnofGraphoBonitsg 351
3.2 OpmitalaettrnPeSarch 353
3.3 oCmpuaotitnalExpermienst 354
3.4 ealetdRorkW 355
4. AppcilaoitnsofGraphcfiaoiitsnalsC 358
5. LabelrPopagaoitn 358
6. oCnculdnigemRarks 359
efRerences 359
12
MninigGraphaettrnsP 365
HongCheng, XifengYanandJiaweiHan
1. Inrtoducoitn 366
2. rFequentuSbgraphMninig 366
2.1 rPobelmDenfioitin 366
2.2 Aproir-ibeadsApproach 367
2.3 aettrwhtn-PGroApproach 368
2.4 oledCsandMaxmialuSbgraphs 369
2.5 MniniguSbgraphsnianiSgelGraph 370
2.6 TheoCmpuaotitnaloelBtnteck 371
3. MniniggiSncfiaintGraphaettrnsP 372
3.1 rPobelmDenfioitin 372
3.2 gboo:tsAraBnch-ando-BundApproach 373
x
MANAGINGANDMININGGRAPHDATA
3.3 gL:PSAaraitlPLetasqSuaresgoirsneesRApproach 375
3.4 LE:APArtSucutralLeapeSarchApproach 378
3.5 GraphgiS:AeFautreepRreensaotitnApproach 382
4. MninigevepRreensatitOrhtogonalGraphs 385
4.1 rPobelmDenfioitin 386
4.2 anRdomziedMaxmialuSbgraphMninig 387
4.3 OrhtogonalevepRrenesatiteStGeneraoitn 388
5. oCnculoisns 389
efRerences 389
13
AyuServonrtSeamnigAglorhtimsforeviMsasGraphs 393
JianZhang
1. Inrtoducoitn 393
2. rtSeamnigModelforeviMsasGraphs 395
3. citsastitSandoCunnitgraingelsT 397
4. GraphMacthnig 400
4.1 UnwegihetdMacthnig 400
4.2 egihetdWMacthnig 403
5. GraphatnDsice 405
5.1 atnDsiceApproxmiaoitnunisgMupitlelessasP 406
5.2 atnDsiceApproxmiaoitnniOnesasP 411
6. anRdomaklsWonGraphs 412
7. oCnculoisns 416
efRerences 417
14
AyuServofaoiytn-arcPeersvvrPiofGraphsandoScailorkNeswt 421
XintaoWu, XiaoweiYing, KunLiuandLeiChen
1. Inrtoducoitn 422
1.1 yacvrPiniuPbhsinligoScailorNekwts 422
1.2 ackBgroundweldgKneo 423
1.3 ytilUitaoitnrPeresv 424
1.4 AnoynmziaoitnApproaches 424
1.5 Noaotitns 425
2. yacvrPiaAttcksonevNaiAnoynmziedorNkewts 426
2.1 evAcitaAttcksandevisasPaAttcks 426
2.2 rtSucutralQuereis 427
2.3 OhteraAttcks 428
3. 𝐾-AnoynmytiyacvrPiaoitnrPeersvvaiEdgeModcfiaoiitn 428
3.1 𝐾g-rDeeeGenerazilaoitn 429
3.2 𝐾-NegihborhoodAnoynmyti 430
3.3 𝐾-AuotmorphmsiAnoynmyti 431
4. yacvrPiaoitnrPeersvvaianRdomziaoitn 433
4.1 eilniescReotrtSucutralaAttcks 434
4.2 LnikcoluDsisreAnaylsis 435
4.3 ecoRnrtuscoitn 437
4.4 eFautrerPeersvniganRdomziaoitn 438
5. yacvrPiaoitnrPeersvvaiGenerazilaoitn 440
6. AnoynmzinigcihRGraphs 441
xi
Contents
6.1 LnikrPoetcoitnnicihRGraphs 442
6.2 AnoynmzinigpiBaretitGraphs 443
6.3 AnoynmzinigcihRInetracoitnGraphs 444
6.4 AnoynmzinigegihetdEdge-WGraphs 445
7. OhteryacvrPiuIsessniOnnileoScailorNkewts 446
7.1 vnigDeriLnikrtSucutreofhteEnriteorNekwt 446
7.2 vnigDerieProsnalIdenfitynigInformaoitnfromoScailNe-t
orkwnigetisS 448
8. oCnculoisnanduFutreorkW 448
weldAckgnmoenst 449
efRerences 449
15
AyuServofGraphMninigforebWAppcilaoitns 455
DeboraDonatoandAristidesGionis
1. Inrtoducoitn 456
2. rPemilniareis 457
2.1 LnikAnaylsisanRknigAglorhtims 459
3. MninigHgih-QuyatilIetms 461
3.1 rPedcoiitnofuSfccsueslIetmsniaoC-caotiitnorNkewt 463
3.2 niFdnigHgih-QuyatiloCnetntni Quoitesn-Anwersnig-oPr
atsl 465
4. MninigQueryLogs 469
4.1 cDerspioitnofQueryLogs 470
4.2 QueryLogGraphs 470
4.3 QueryecoRmmendaoitns 477
5. oCnculoisns 480
efRerences 481
16
GraphMninigAppcilaoitnsotoScailorNekwtAnaylsis 487
LeiTangandHuanLiu
1. Inrtoducoitn 487
2. GraphaettrnsPnigLae-rcSaelorNkewts 489
2.1 cSael-rFeeorNkewts 489
2.2 ordlmSa-llWfectEf 491
2.3 oCmmunytirtSucutres 492
2.4 GraphGeneraotrs 494
3. oCmmunytiDeetcoitn 494
3.1 Nodee-nCrtcioCmmunytiDeetcoitn 495
3.2 Groupe-nCrtcioCmmunytiDeetcoitn 498
3.3 orNekwte-nCrtcioCmmunytiDeetcoitn 499
3.4 Heirarchye-nCrtcioCmmunytiDeetcoitn 504
4. oCmmunytirtSucutreaulaoitnEv 505
5. eeasrRchuIsess 507
efRerences 508
17
aorSeuf-wtBgLocazilaoitnhwtiGraphMninig 515
FrankEichingerandKlemensBo-hm
1. Inrtoducoitn 516
2. cisasBofallCGraphedasBuBgLocazilaoitn 517