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Overlapping Community Detection in Dynamic Networks Qinna Wang Overlapping community detection in dynamic networks Qinna Wang To cite this version: Qinna Wang. Overlapping community detection in dynamic networks. Other [cs.OH]. Ecole normale supérieure de lyon - ENS LYON, 2012. English. NNT : 2012ENSL0713. tel-00701217 HAL Id: tel-00701217 https://tel.archives-ouvertes.fr/tel-00701217 Submitted on 24 May 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THESE` en vue d’obtenir le grade de Docteur de l’Ecole Normale Sup´erieure de Lyon Sp´ecialit´eInformatique Universit´ede Lyon Laboratoire de l’Informatique du Parall´elisme Ecole´ doctorale Informatique et Math´ematiques pr´esent´eeet soutenue publiquement le ! Avril !# ! par Qinna Wang $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$% D´etection de communaut´esrecouvrantes dans des r´eseaux de terrain dynamiques $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$% devant la commission d’examen compos´eede Rapporteurs: Anne-Marie Kermarrec) D&) Inria Rennes(*retagne "tlantique Matthieu Latapy) D&) ,NRS - UPM, Examinateurs' Pablo Jensen) D&) ,NRS - ENS de Lyon Bertrand Jouve) Professeur) Universit´eLumi/ere Lyon ! Christophe Prieur) Md,) Universit´eParis Diderot Directeur de th/ese: Eric Fleury) Professeur, ENS de Lyon aa 0 Abstract In complex net1orks) the notion of community structure refers to the presence of groups of nodes in a net1or23 4hese groups are more densely connected internally than with the rest of the net1or23 4he presence of communities inside a net1ork gives an insight on net1or2 structural properties3 5or e.ample) in social net1or2s, communities are based on common interests) location, hobbies3333 6enerally) a community structure is described by a partition of the net1or2 nodes) where each node belongs to a unique com- munity3 " more reasonable description seems to be overlappin+ community structure, where nodes are allo1ed to be shared by several communities3 Moreover) 1hen con- siderin+ dynamic net1orks whose interactions bet1een nodes evolve in time, it appears crucial to consider also the evolution of the intrinsic community structure. This thesis focus on minin+ dynamic community evolution and overlappin+ com( munity detection. 7e have proposed t1o distinct methods for overlapping community detection. The 8rst one named clique optimization and the second one called fuzzy detection. :ur clique optimization aims to identify granular overlaps and it is a 8ne grain scale approach3 :ur fu99y detection is at a coarser grain scale 1ith the strategy of identifying modular overlaps3 Their applications in synthetic and real net1orks indicate that both methods can be used for characteri9in+ overlappin+ nodes but in distinct and complementary views. 7e also propose the definition of predecessor and successor in mining community evolution3 Such definition describes the relationship bet1een com( munities at different time steps. 7e use it to detect community evolution in dynamic net1or2s and sho1 ho1 modular overlaps evolve over time. " visuali9ation tool called lineage diagrams is used to sho1 community evolution by connectin+ communities in relationship of predecessor and successor. Several cases are studied. Keywords: community detection, overlappin+ community structure) complex net( 1or2s, dynamic net1or2s, community evolution, net1or2 science R´esum´e Dans le conte.te des r´eseaux comple.es, la structure communautaire du r´eseau de- vient un su<et important pour plusieurs domaines de recherche. Les communaut´essont en +´en´eral vues comme des groupes int´erieurement denses3 La d´etection de tels groupes offre un ´eclairage int´eressant sur la structure du r´eseau3 Par exemple) une communaut´e de pages 1eb regroupe des pages traitant du m=eme sujet3 La d´efinition de commu( naut´es est en +´en´eral limit´ee/aune partition de l’ensemble des nœuds3 Cela exclut par d´efinition qu’un n>ud puisse appartenir /aplusieurs communaut´es) ce qui pourtant est naturel dans de nombreux ?cas des r´eseau. sociau. par exemple@3 Une autre question importante et sans r´eponse est l’´etude des r´eseau. et de leur structure communautaire en tenant compte de leur dynamique. Cette th/ese porte sur l’´etude de r´eseau. dynamiques et la d´etection de communaut´esrecouvrantes3 Nous proposons deux m´ethodes di;´erentes pour la d´etection de communaut´es re- couvrantes. La premi/ere m´ethode est appel´ee optimisation de clique3 L’optimisation de clique vise /ad´etecter les n>uds recouvrants granulaires3 La m´ethode de l’optimisation de clique est une approche /agrain 8n3 La seconde m´ethode est nomm´ee d´etection Aoue ?fu99y detection@3 Cette m´ethode est /agrain plus grossier et vise /aidentifier les groupes recouvrants3 Nous appliquons ces deux m´ethodes /ades r´eseaux synth´etiques et r´eels3 Les r´esultats obtenus indiquent que les deux m´ethodes peuvent =etre utilis´ees pour caract´eriser les nœuds recouvrants3 Les deux approches apportent des points de vue distincts et compl´ementaires. Dans le cas des +raphes dynamiques, nous donnons une d´efinition sur la relation entre les communaut´es/adeux pas de temps cons´ecutif. ,ette technique permet de repr´esenter le changement de la structure en fonction du temps3 Pour mettre en ´evidence cette relation, nous proposons des diagrammes de lignage pour la visualisation de la dynamique des communaut´es3 Ces diagrammes qui connectent des communaut´es/ades pas de temps successifs montrent l’´evolution de la structure et l’´evolution des groupes recouvrantes3 Nous avons ´egalement appliquer ces outils /ades cas concrets. Mots cl´es: structure communautaire) communaut´es recouvrantes, r´eseau. de terrain dynamiques) ´evolution de communaut´es) r´eseaux comple.es Remerciements Be remercie) en premier lieu, mes rapporteurs, Mme Anne-Marie Cermarrec et Mr3 Matthieu Latapy) pour avoir accept´ela t=ache de rapporter ma th/ese3 Be remercie ´egalement Mr3 ,hristophe Prieur) M3 *ertrand Bouve et Mr3 Pablo Jensen d’avoir accept´ede prendre part /amon <ury3 Au cours des trois ann´ees qu’a dur´ema th/ese, <’ai eu le plaisir de rencontrer un grand nombre de chercheurs, d’enseignants et d’´etudiants) avec lesquels <’ai eu le tr/es grand plaisir de travailler tout au long de cette th/ese. C’est /aeux que vont mes plus grands remerciements3 Be leur adresse ma gratitude pour l’attention, les conseils) les encouragements, la patience, l’amabilit´edont ils ont fait preuve tout au long de mes travaux3 Be remercie) M. Eric 5leury pour m’avoir offert l’opportunit´ede r´ealiser cette th/ese3 Il a diri+´emon travail avec une grande justesse, une profonde humanit´eet beaucoup de gaiet´e) ce pour quoi je le remercie infiniment3 Be remercie en particulier les membres de l’´equipe D(NET ' 6uillaume Chelius) Andreea Chis, Christophe ,respelle, Adrien 5riggeri) Lucie Martinet, S/everine Morin et Evelyne Blesle. Be remercie chaleureusement mes coll/egues de l’Universit´ede Paris D' Bean-Loup Guillaume et 4homas Aynaud3 Enfin) <e souhaiterais remercier mes parents) tous les amis et les personnes qui ont toujours encourag´eet accompagn´emon travail de leur pens´eepositive3 Contents Introduction 9 1 Community detection in dynamic networks 13 3 Communities in net1or2s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 3 3 Definitions of community 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 E 3 3! Community structure 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 F 3! Community evolution in dynamic net1or2s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 G 3!3 Communities in dynamic graphs 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 H 3!3! Community dynamics 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 H 30 Community detection in dynamic net1or2s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 !! 303 Dynamic community detection challenges 3 3 3 3 3 3 3 3 3 3 3 3 3 !E 303! 41o-stage approaches 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 !I 3030 Evolutionary clusterin+ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 303E Couplin+ graph clusterin+ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0E 3E Benchmar2s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0F 3E3 Benchmark graphs 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0F 3E3! Real net1or2s 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0I 3E30 Comparing partitions 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0H 3F Conclusion 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 333333333333333333 E 2 Overlapping communities and modularity 42 !3 Related 1ork on cover detection 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 E0 !3! Modi8ed modularity for covers 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 EE !3!3 " novel modularity 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 EE !3!3! Existin+ modularity for covers 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 EG !30 Clique optimi9ation 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 F# !303 :ur proposed definition 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 F# !303! The clique optimization algorithm 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 F! !3030 Benchmark graphs 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 FE !3E 5uzzy detection 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
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