1. H Epistmh twn DiktwnMia Pol Sntomh Eisagwgik ParousashMwusc A. MpountourdhcTmma Majhmatikn Panepisthmou Patrnmboudour@upatras.grOktbrioc 2014Mwusc A. Mpountourdhc H Epistmh twn Diktwn

2. PerieqmenaBasikc 'Ennoiec DiktwnMia Panoramik 'Ekjesh Diktuakn 'ErgwnLga Endeiktik Paradegmata Diktuakn UpologismnEndeiktiko ProiMwusc A. Mpountourdhc H Epistmh twn Diktwn 3. Basikc 'Ennoiec DiktwnMwusc A. Mpountourdhc H Epistmh twn Diktwn 4. Ti enai na dktuo;Praktik, tsi pwc katalabanoume ennoiologik tienai na dktuo:'Ena dktuo enai na snolo paragntwn forwndrshc, pou onomzontai drntec (actors), oi opooisqetzontai metax touc me kpoia morfmatadiadrastikc sumperiforc, pou onomzontaidesmo (ties) sqseic didrashc (interactions).Tupik, tsi pwc analetai majhmatik (sthn JewraGrfwn [Graph Theory]) kai anaparstatai mswgrafikn optikopoisewn (visualizations):'Ena dktuo enai na snolo kmbwn ( korufn shmewn), oi opooi sundontai metax touc mekpoia sugkekrimna morfmata sundsmwn (links).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 5. Kathgoriopoiseic Diktuakn DrntwnOi drntec enc diktou mpore na enai:'Atoma (njrwpoi) me diaforetik dhmografikqarakthristik (pwc flo, fuljnoc, uphkothta,hlika, ekpadeush, ergasa, oikonomik katstash, katoikaklp.) se diaforetikc yuqoswmatikc katast-seic [pq., asjneiec, ugea, broc, eutuqa klp.] me diafo-retikc idecpepoijseictopojetseicprotimseicgia kpoia politistik politik oikonomik klp. zhtmata.Omdec atmwn (pwc organseic, etairec, jesmik smata,krth klp.).Organismo (zwiko biologiko).Ulik prgmata (pwc bibla, ergasec, episthmonikokldoi, msa epikoinwnacplhrofrhshc, teqnourgmata[artifacts], emporemata, mhqanc, upologistc, diadiktuakst/seldec klp.).Sunajroistik gegonta (pwc sumfwnec, yhfoforec,ekjseic, diadhlseic diamarturac, sumbnta, peristseic,taktikc sunantseic se qrouc epikoinwnac atmwn organsewn gia sugkekrimnouc skopoc klp.).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 6. Kathgoriopoiseic Diktuakn DiadrsewnOi diadrseic se na dktuo mpore na enai:Koinwnikc sqseic metax atmwn (pwc filac,suggneiac, sunaisjhmatikc fshc, sexoualikc sqshc,arskeiacdusarskeiac, empistosnhcduspistac klp.).Koinwnikc sqseic allhlexrthshc (pwc didsko-ntadidaskmenou, prostmenouufistmenou, sunergasac,upostrixhc, allhlobojeiac, paroqc sumbouln,emporiknoikonomikn sunallagn klp.).Koinwnikc sqseic antipalthtac (pwc diafwnac,antiparajsewn, qjrac, fbou, antagwnismo klp.).'Emmesec sqseic diamoirasmo summetoqc sekoin gegonta (pwc se organseic, sumbnta,lsqecklamp, sullgouc, sumbolia, sqolea,jesmocidrmata, katagwgc diamonc se gewgrafikcperioqc, sundhmosiesewn, bibliografikn anaforn,didoshc gnshc, koinwnikc epirroc, koinn asqolin,epanalambanmenwn sunhjein, pwc qrshc narkwtikn, klp.,metdoshc [contagion] asjenein k.. diqushc in k.. klp.).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 7. Qarakthristik Drntwn kai DiadrsewnDiaforetikc kathgorec ( tpoi) drntwn diadrsewn mporonna enopoihjon se omdec, stic opoec orzetai na qarakthristik(attribute), pou parnei diaforetikc timc se kje omda.Genikc, kje qarakthristik mpore na jewrhje wc mia metablht,ete posotik (suneqn diakritn timn) poiotik (diataktikn[ordinal] onomastikn] [nominal] timn). P.q.:'Arrenec kai jleic drntec omadopoiontai ktw ap to(poiotik) onomastik qarakthristik tou flou.Drntec diaforetiko brouc omadopoiontai ktw ap to(posotik) suneqc qarakthristik tou brouc.Diadrseic hlektronikc epikoinwnac omadopoiontai ktw apto (posotik) diakrit qarakthristik tou pljouc thcsuqnthtac twn antallassmenwn mhnumtwn (se kpoiaperodo).Diadrseic diaforetikn bajmn thc sqshc filac omadopoio-ntai ktw ap to (poiotik) diataktik qarakthristik thcdiabjmishc thc ntashc thc sqshc filac.Diadrseic sumpjeiacantipjeiac omadopoiontai ktw apto (poiotik) diataktik (duadik) qarakthristik touprshmou (jetiko arnhtiko) thc sqshc.Oi antstoiqoi grfoi enai oi grfoi me brh (timc) (weightedvalued graphs) stouc kmbouc stouc sundsmouc. Eidik sto teleu-tao pardeigma, onomzontai proshmasmnoi grfoi (signed graphs).'Ena dktuo, sto opoo oi dioi drntec diathron perissterec thcmiac diaforetikc diadrseic onomzetai polusqidc (multiplex).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 8. Diktuakc Analseic1 Koinwnik Diktuak DedomnaErwthmatolgia kai sunentexeicIstorik arqea kai arqea tpouBibliometrik kai episthmometrik dedomnaDedomna ap to Internet (mhnmata, istoseldec,mplogk, koinwnik msa)Sqesiak Megla Dedomna (Big Data) kai AnoiktDedomna (Open Data)2 Diktuak MtraBajmo kmbwn IstogrmmataKentrikthtec kmbwnSuntelestc sussreushc kai metabatikthtaAmoibaithta sundsmwnApostseic kmbwnMwusc A. Mpountourdhc H Epistmh twn Diktwn 9. 3 Diktuako diamerismoSunektikc sunistsec kai klkeckpurnecPurnacperifreiaIsodunamec kmbwn (domik kai kanonik)Omadopohsh se mplok BlockmodelingKointhtec (Communities)Taxinomhsimthta (assortativity) kai anmeixh (mixing)4 Qronikc Exartmena DktuaTroqic metabsewn5 Statistik Jewra DiktwnExponential Random Graph Models (ERGM)6 Montelopoiseic DiktwnKoinwnik epirroDiqush (montla SIR kai SIS)Tuqaoi grfoi ErdosRe nyiDktua mikrn ksmwn (smallworlds)Dktua qwrc klmaka (scalefree)Auxanmena tuqaa dktua kai to montloBara basiAlbertMwusc A. Mpountourdhc H Epistmh twn Diktwn 10. Mia Panoramik 'Ekjesh Diktuakn'ErgwnMwusc A. Mpountourdhc H Epistmh twn Diktwn 11. To Dktuo twn Flwrentiann OkwnSqma: To dktuo twn gmwn metax twn meglwn Okwn thcFlwrentac tou mesawna (Padgett & Ansell, Robust action and the rise of theMedici, 14001434, American Journal of Sociology, 1993, 98(6): 12591319).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 12. To Dktuo twn Stenn Sunergatn tou SantmSqma: To dktuo tou eswteriko kklou twn stenn sunergatn touSantm Qousen (Baraba si et al., Network Science Book,http://barabasilab.neu.edu/networksciencebook/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 13. Dktuo Filac Meln Lsqhc KarteSqma: Dktuo filac twn 34 meln miac Panepisthmiakc lsqhc karte(Zachary, An information flow model for conflict and fission in small groups,Journal of Anthropological Research, 1977, 33: 452473).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 14. Dktuo Sunaisjhmatikn SqsewnSqma: Dktuo sunaisjhmatiknerwtikn sqsewn (Bearman et al.,Chains of affection: The structure of adolescent romantic and sexual networks,American Journal of Sociology, 2004, 110: 4491)se optikopohsh tou MarkNewman (http://www-personal.umich.edu/~mejn/networks/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 15. To dktuo twn Ajlwn tou Bktwroc OugkSqma: To dktuo twn sqsewn metax twn kriwn qaraktrwn twnAjlwn tou Bktwroc Ougk (ta qrmata antistoiqon se kointhtec, pouupologsjhkan ek twn ustrwn) (Newman & Girvan, Finding and evaluatingcommunity structure in networks, Physical Review E, 2004, 69: 026113).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 16. Kuriarqontec kmboi kai kointhtec stodktuo twn AjlwnMwusc A. Mpountourdhc H Epistmh twn Diktwn 17. Dktuo Paqsarkwn AtmwnSqma: Dktuo paqsarkwn atmwn (Christakis & Fowler, The spread ofobesity in a large social network over 32 years, New Englnd Journal of Medicine,2007, 357(4): 370379)[Mgejoc kmbwn BMI, ktrinoi paqsarkoi,prsino mh paqsarkoi, mwb sundseic fila, portokal suggenec.]Mwusc A. Mpountourdhc H Epistmh twn Diktwn 18. Dktuo Eutuqismnwn AtmwnSqma: Dktuo eutuqismnwn atmwn (Fowler & Christakis, Dynamic spreadof happiness in a large social network: Longitudinal analysis over 20 years in theFramingham Heart Study, British Medical Journal, 2008, 337(768): a2338).Kmboi tetragwniko gunakec, kukliko ndrec, mple ligtero eutuqec,ktrino perisstero eutuqec, kkkinec sundseic fila, marec suggenec.]Mwusc A. Mpountourdhc H Epistmh twn Diktwn 19. Dktuo Filac Majhtn tou Faux Magnolia High SchoolSqma: To dktuo filac 1461 majhtn tou Faux Magnolia High Schoolqwrc apomonwmnouc kmbouc (Goudreau et al., A statnet Tutorial, Journal ofStatistical Software, 2008, 24(9): 127).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 20. Dktuo Filac Majhtn tou Faux Magnolia High School me toQarakthristik tou 'Etouc Fothshc twn MajhtnSqma: To dktuo filac 1461 majhtn tou Faux Magnolia High School meto qarakthristik tou touc fothshc twn majhtn kai qwrcapomonwmnouc kmbouc (Goudreau et al., A statnet Tutorial, Journal ofStatistical Software, 2008, 24(9): 127).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 21. Dktuo Filac me to Qarakthristik thc Fulc twn MajhtnSqma: 'Ena dktuo filac majhtn me to qarakthristik thc fulc twn majhtn (ktrino =leuko, prsino = maroi, kkkino = llhc fulc) kai qwrc apomonwmnouc kmbouc (Moody, Race,school integration, and friendship segregation in America, American Journal of Sociology, 2001, 107:679716)se optikopohsh tou Mark Newman (http://www-personal.umich.edu/~mejn/networks/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 22. Dktuo Sunergasac sthn Santa FeSqma: Dktuo sunergasac episthmnwn tou Institotou Santa Fe (Girvan& Newman, Community structure in social and biological networks, Proceedings ofthe National Academy of Sciences of the USA, 2002, 99: 82718276).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 23. Dktuo Parapompn sthn KoinwniologaSqma: Dktuo bibliografikn parapompn sthn Koinwniologa ap dedomna tou Jim Moody(http://orgtheory.wordpress.com/2009/08/14/sociologys-citation-core/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 24. To Dktuo twn Qwrn me Meglo QrocSqma: To dktuo twn qwrn me megla qrh (Baraba si et al., NetworkScience Book, http://barabasilab.neu.edu/networksciencebook/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 25. Trofikc Istc tou Oikosustmatoc miac LmnhcSqma: To dktuo tou trofiko isto (food web) tou oikosustmatoc thcLmnhc Little Rock tou Wisconsin (Martinez, Artifacts or attributes? Effects ofresolution on the Little Rock Lake food web, Ecological Monographs, 1991, 61:367392).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 26. Dktuo Fainotupikn AsjeneinSqma: Dktuo fainotupikn asjenein (Hidalgo, Blumm, Baraba si &Christakis, A Dynamic Network Approach for the Study of Human Phenotypes,PLOS Computational Biology, http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1000353).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 27. To InternetSqma: To dktuo twn ISPs tou Internet (Cheswick & Burch, Internet Atlas Gallery,http://www.caida.org/projects/internetatlas/gallery/ches/data.xml).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 28. To FacebookSqma: To dktuo epikoinwnac tou Facebook (Baraba si et al., NetworkScience Book, http://barabasilab.neu.edu/networksciencebook/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 29. Dktuo TwitterSqma: H gigantiaa sunektik sunistsa enc diktou Twitter giakpoia RTs (retweets) pou ginan anaforik me ta gegonta diamarturacsthn Tourka ton Ionio tou 2013.Mwusc A. Mpountourdhc H Epistmh twn Diktwn 30. Dktuo LinkedInSqma: Oi koino moirasmnoi (shared) floi gia duo qrstec touLinkedIn.Mwusc A. Mpountourdhc H Epistmh twn Diktwn 31. Dktuo (Dia)Kleidwmnwn DS Etairin(Interlocking Directorates)Sqma: Dktuo (Dia)Kleidwmnwn (Interlocking Directorates) Dioikhtikn Sumboulwn Etairinap koinc summetoqc steleqn se autc(http://orgtheory.wordpress.com/2011/08/19/theyrule-net-interlocking-boards/,http://theyrule.net/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 32. To Dktuo BioteqnologacBiomhqanac sticHPASqma: To dktuo twn sqsewn BioteqnologacBiomhqanac stic HPA (Powell, White, Koput &OwenSmith, Network Dynamics and Field Evolution: The Growth of Interorganizational Collaboration in theLife Sciences, American Journal of Sociology, 2005, 110(4): 11321205,http://eclectic.ss.uci.edu/~drwhite/Movie/).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 33. Dktuo Summetoqn se Koinwnikc EkdhlseicGunaikn tou NtouSqma: Dktuo summetoqnmazxewn se 14 sumbnta koinwniknekdhlsewn 18 gunaikn tou Ameriknikou Ntou (Davis, Gardner & Gardner,Deep Douth, University of Chicago Press, 1941).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 34. Dktuo Yhfoforin sto Antero Dikastriotwn HPASqma: Dktuo yhfoforin sto Antero Dikastrio twn HPA me tic suneqmenec grammc nasumbolzoun jetikc yfouc kai tic diakoptmenec grammc arnhtikc yfouc (Mrvar & Doreian,Partitioning signed twomodenetworks, Journal of Mathematical Sociology, 2009, 33: 196221).Mwusc A. Mpountourdhc H Epistmh twn Diktwn 35. Dktuo Epitropn sthn Boul twnAntiprospwn twn ARTICLE HPAIN PRESSBUDGETVETERANS AFFAIRSARMED SERVICESAGRICULTURE420 M.A. Porter et al. / Physica A 386 (2007) 414438APPROPRIATIONSINTELLIGENCEHOUSE ADMINISTRATIONENERGY/COMMERCEOFFICIAL CONDUCTHOMELAND SECURITYGOVERNMENT REFORMWAYS AND MEANSINTERNATIONAL RELATIONSTRANSPORTATIONSMALL BUSINESSEDUCATIONSCIENCEFINANCIAL SERVICESRULESRESOURCESJUDICIARYSqma: Fig. 4. (Color) Network of committees (squares) and subcommittees (circles) in the 108th US House of Representatives, color-coded bythe Dktuo parent standing epitropn and select committees. (tetrgwna(The depicted ) labels kai indicate upothe epitropn parent committee (of kkloieach group ) sthn but do not 108identify h Boul thetwnAntiprospwn location twn of that HPA committee (Porter, in the plot.) Mucha, As with Fig. Newman 2, this visualization & Friend, was produced Community using a variant of the KamadaKawai springembedder, with link strengths (again indicated by darkness) determined by normalized interlocks. Observe structure again that subcommittees in the United of theStatesHouse of Representatives, same parent committee Physica are closely A, connected 2007, to each 386: other.414438).Oi sundseic anapariston koincsummetoqc bouleutn se (upo)epitropc.Mwusc A. Mpountourdhc H Epistmh twn DiktwnSecurity Committee shares only one common member (normalized interlock 2.4) with the Intelligence SelectCommittee (located near the 1 oclock position in Fig. 5) and has no interlock at all with any of the four 36. Lga Endeiktik ParadegmataDiktuakn UpologismnMwusc A. Mpountourdhc H Epistmh twn Diktwn 37. Basiko Sumbolismo Jewrac Grfwn'Enac grfoc G enai na zegoc (V, E), pou to V enaina snolo korufn ( kmbwn shmewn) kai to Eenai na snolo akmn ( grammn sundsmwn sundsewn).'Etsi, o grfoc grfetai wc G = (V, E) ki, tan qreizetai na epishmnoumeti to V enai to snolo korufn tou grfou G, grfoume V = V(G) kai,parmoia, ti to E enai to snolo akmn tou G, grfoume E = E(G).Kje akm e 2 E enc grfou G = (V, E) antistoiqe se duo korufc tousunlou V, oi opoec apotelon ta duo kra thc akmc. 'Otan ta kra thcakmc e 2 E enai oi korufc u kai v 2 V, grfoume e = (u, v). Shmeiwton tioi akmc den qoun katejunsh, dhlad, e = (u, v) = (v, u).O grfoc G = (V, E) me V = fv1, v2, v3, v4g kai E = f(v1, v3), (v2, v3), (v3, v4)g:a pair (V,E), where V is a set of vertices (also called points), and E called lines).number of vertices is called the order of a graph and the number of edges is called graph.graph G = (V,E) the vertex set V is often denoted V (G) and the edge set E e E is associated with a pair of points from V . If u and v are associated they are called the endpoints of e, we often write uv or {u, v} to represent 2v1 v2 v4 v3V = {v1, Mwusc v2, Av3}, . Mpountourdhc E = {{v3, H Epistmh v4}, {v2, twn v3}, Diktwn{v1, v3}} 38. observe that G1 G2 = G1 G2. However, usually for ring sums we have the same vertexTpoi Grfwn= V2, but different edge sets E1= E2, whereas for unions we often want disjoint unions, = .be aware that notations for these operations vary. In particular, some authors use G1 G2,join and take G1 + G2 to be a disjoint union.'Enac brqoc (loop) enai mia akm pou ennei mia koruf v me toneaut thc, e = (v, v).Duo ( perissterec) akmc onomzontai parllhlec an ta kra toucenai oi diec korufc.'Enac grfoc qwrc brqouc kai qwrc parllhlec akmc onomzetaiaplc, en diaforetik onomzetai pollaplc grfoc (multigraph).'Enac grfoc onomzetai grfoc me brh (weighted graph) kaisumbolzetai wc G = (V, E,w), an se kje akm tou e antistoiqe nabroc mia tim w(e) 2 R.Directed GraphsDefinition 10directed graph or digraph is a pair (V,E), where V is a set of points (also called vertices),and E is a set of ordered pairs of points from V called arcs.'Enac kateujunmenoc grfoc digrfoc G enai na zegoc (V, E), pou toV enai na snolo korufn ( kmbwn shmewn) kai to E enai nasnolo txwn me to kje txo e 2 E na antistoiqe se na diatetagmnozegoc korufn (u, v) tsi ste na kateujnetai ap thn koruf u procthn koruf v.O kateujunmenoc grfoc G = (V, E) me V = fv1, v2, v3, v4g kai E = f(v1, v3), (v3, v2), (v4, v3)g:Each arc e E is associated with an ordered pair of points from V . If u and v are associatedwith the edge e they are called the endpoints of e, we often write uv or (u, v) to represent thearc e.Example 11v1 v4 v2v3V Mwusc = {v1, A. v2, Mpountourdhc v3}, E = {(v4, H v3), Epistmh (v3, twn v2), Diktwn(v1, v3)} 39. Dimerec Grfoi'Enac grfoc onomzetai dimerc(bipartite), tan uprqei nacdiamerismc tou sunlou twnkorufn tou V se duo mrh(tmmata), to U kai to W, dhlad,V = U [W (pou U W = ?), tsiste lec oi akmc na phganounap to U sto W kai na mhnuprqei kami akm ote metaxkorufn tou U ote metaxkorufn tou W.Probolc dimeroc grfou:u1u3u2u4u1u2u3u4w1w2w3 w2w1w312211 212Mwusc A. Mpountourdhc H Epistmh twn Diktwn 40. Bajmo KmbwnGetonec: 'Estw o mh kateujunmenoc grfoc G = (V, E) kai i, j 2 Vduo korufc tou. H j lgetai getonac thc i tan (i, j) 2 E.Pnakac Geitnashc (Adjacency Matrix): Enai nac(summetrikc) pnakac A = fAgi,j2V txhc jVjjVj ttoioc steA = 1, tan i, j getonec, A = 0, diaforetik.Bajmo: Sto mh kateujunmeno grfo G, o bajmc miac korufc i,pou sumbolzetai wc ki, orzetai san to pljoc twn geitnwn tou i,dhlad, to pljoc twn sundsewn pou prospptoun sto i.Profanc, isqei:ki =Xj2VA =Xi2VAki, epiplon,Xi2Vki =Xi,j2VA = 2jEjMwusc A. Mpountourdhc H Epistmh twn Diktwn 41. 'Estw tra o kateujunmenoc grfoc G = (V, E), gia ton opoon oantstoiqoc pnakac geitnashc A = fAg enai mh summetrikc.O bajmc eisdou thc korufc i tou G, pou sumbolzetai wc kin i ,orzetai san to pljoc twn sundsewn pou xekinon ap getonectou i kai kateujnontai proc ton i, dhlad,kini =Xj2VAO bajmc exdou thc korufc i tou G, pou sumbolzetai wc kout i ,orzetai san to pljoc twn sundsewn pou xekinon ap ton i kaikateujnontai proc getonec tou i, dhlad,kouti =Xi2VAProfanc, isqei:Xi2Vkini =Xj2Vkouti =Xi,j2VA = jEjMwusc A. Mpountourdhc H Epistmh twn Diktwn 42. Bajmo kmbwn sto dktuo karteMwusc A. Mpountourdhc H Epistmh twn Diktwn 43. Geniko Tpoi Diktuakn Katanomn BajmnSqma: Diwnumik Katanom ( Katano-m Poisson) gia tuqaouc grfouc ErdosRe nyiSqma: Katanom Nmou Dnamhc (PowerLaw) gia dktua qwrc klmaka (scalefreenetworks)Mwusc A. Mpountourdhc H Epistmh twn Diktwn 44. Kentrikthtec Kmbwn:1. Kentrikthta Bajmo (Degree Centrality)Oi orismo OLWN twn kentrikthtwn pou ja dsoumeed kai sth sunqeia aforon mh kateujunmenouc(aploc) grfouc.H kentrikthta bajmo (degree centrality) xi tou kmboui isotai proc ton bajm ki tou kmbou auto:xi = kix8 = 5Mwusc A. Mpountourdhc H Epistmh twn Diktwn 45. 2. Kentrikthta Endiamesthtac(Betweenness Centrality)H kentrikthta endiamesthtac (betweenness centrality) xi tou kmboui isotai proc:xi =Xs6=i6=t2Vnistgstpou nist enai to pljoc twn gewdaitikn diadromn metax twnkmbwn s kai t, pou pernon ap ton kmbo i, kai gst enai to sunolikpljoc twn gewdaitikn diadromn metax twn kmbwn s kai t.n23,23 = 2g3,23 = 4x2 = 0.1436Mwusc A. Mpountourdhc H Epistmh twn Diktwn 46. 3. Kentrikthta Eggthtac(Closeness Centrality)Se nan grfo G, gia kje duo kmbouc i, j, h (gewdaitik) apstastouc d(i, j) orzetai wc to mkoc thc suntomterhc diadromc ap to isto j, efson oi kmboi auto enai sundedemnoi, en d(i, j) = 1,diaforetik (kai fusik, d(i, i) = 0). (H suntomterh diadrommetax duo kmbwn enai h diadrom pou qei to elqisto mkocanmesa se lec tic diadromc metax twn duo kmbwn.)Se nan grfo me n kmbouc, h kentrikthta eggthtac (closenesscentrality) xi tou kmbou i isotai proc:xi =n Pj2V d(i, j)x0 = 0.5689x2 = 0.5593x33 = 0.55x31 = 0.5409Mwusc A. Mpountourdhc H Epistmh twn Diktwn 47. 4. Kentrikthta Idiodiansmatoc(Eigenvector Centrality)H kentrikthta idiodiansmatoc (eigenvector centrality) xi tou kmbou iisotai proc:xi =