SlideShare une entreprise Scribd logo
1  sur  57
Télécharger pour lire hors ligne
H Epist mh twn DiktÔwn 
Mia PolÔ SÔntomh Eisagwgik  ParousÐash 
Mwus c A. MpountourÐdhc 
Tm ma Majhmatik¸n PanepisthmÐou Patr¸n 
mboudour@upatras.gr 
Okt¸brioc 2014 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Perieqìmena 
Basikèc 'Ennoiec DiktÔwn 
Mia Panoramik  'Ekjesh Diktuak¸n 'Ergwn 
LÐga Endeiktikˆ ParadeÐgmata Diktuak¸n Upologism¸n 
EndeiktikoÐ Pìroi 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Basikèc 'Ennoiec DiktÔwn 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Ti eÐnai èna dÐktuo; 
Praktikˆ, ètsi ìpwc katalabaÐnoume ennoiologikˆ ti 
eÐnai èna dÐktuo: 
'Ena dÐktuo eÐnai èna sÔnolo paragìntwn   forèwn 
drˆshc, pou onomˆzontai dr¸ntec (actors), oi opoÐoi 
sqetÐzontai metaxÔ touc me kˆpoia morf¸mata 
diadrastik c sumperiforˆc, pou onomˆzontai 
desmoÐ (ties)   sqèseic diˆdrashc (interactions). 
Tupikˆ, ètsi ìpwc analÔetai majhmatikˆ (sthn JewrÐa 
Grˆfwn [Graph Theory]) kai anaparÐstatai mèsw 
grafik¸n optikopoi sewn (visualizations): 
'Ena dÐktuo eÐnai èna sÔnolo kìmbwn (  koruf¸n   
shmeÐwn), oi opoÐoi sundèontai metaxÔ touc me 
kˆpoia sugkekrimèna morf¸mata sundèsmwn (links). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Kathgoriopoi seic Diktuak¸n Dr¸ntwn 
Oi dr¸ntec enìc diktÔou mporeÐ na eÐnai: 
'Atoma (ˆnjrwpoi) me diaforetikˆ dhmografikˆ 
qarakthristikˆ (ìpwc fÔlo, ful –èjnoc, uphkoìthta, 
hlikÐa, ekpaÐdeush, ergasÐa, oikonomik  katˆstash, katoikÐa 
klp.)   se diaforetikèc yuqo–swmatikèc katastˆ- 
seic [pq., asjèneiec, ugeÐa, bˆroc, eutuqÐa klp.]   me diafo- 
retikèc idèec–pepoij seic–topojet seic–protim seic 
gia kˆpoia politistikˆ   politikˆ   oikonomikˆ klp. zht mata. 
Omˆdec atìmwn (ìpwc organ¸seic, etairÐec, jesmikˆ s¸mata, 
krˆth klp.). 
OrganismoÐ (zwikoÐ   biologikoÐ). 
Ulikˆ prˆgmata (ìpwc biblÐa, ergasÐec, episthmonikoÐ 
klˆdoi, mèsa epikoinwnÐac–plhrofìrhshc, teqnourg mata 
[artifacts], emporeÔmata, mhqanèc, upologistèc, diadiktuakˆ 
sˆðt/selÐdec klp.). 
Sunajroistikˆ gegonìta (ìpwc sumfwnÐec, yhfoforÐec, 
ekjèseic, diadhl¸seic diamarturÐac, sumbˆnta, peristˆseic, 
taktikèc sunant seic se q¸rouc epikoinwnÐac atìmwn   
organ¸sewn gia sugkekrimènouc skopoÔc klp.). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Kathgoriopoi seic Diktuak¸n Diadrˆsewn 
Oi diadrˆseic se èna dÐktuo mporeÐ na eÐnai: 
Koinwnikèc sqèseic metaxÔ atìmwn (ìpwc filÐac, 
suggèneiac, sunaisjhmatik c fÔshc, sexoualik c sqèshc, 
arèskeiac–dusarèskeiac, empistosÔnhc–duspistÐac klp.). 
Koinwnikèc sqèseic allhlexˆrthshc (ìpwc didˆsko- 
nta–didaskìmenou, proðstˆmenou–ufistˆmenou, sunergasÐac, 
upost rixhc, allhlobo jeiac, paroq c sumboul¸n, 
emporik¸n–oikonomik¸n sunallag¸n klp.). 
Koinwnikèc sqèseic antipalìthtac (ìpwc diafwnÐac, 
antiparajèsewn, èqjrac, fìbou, antagwnismoÔ klp.). 
'Emmesec sqèseic diamoirasmoÔ   summetoq c se 
koinˆ gegonìta (ìpwc se organ¸seic, sumbˆnta, 
lèsqec–klamp, sullìgouc, sumboÔlia, sqoleÐa, 
jesmoÔc–idrÔmata, katagwg c   diamon c se gewgrafikèc 
perioqèc, sun–dhmosieÔsewn, bibliografik¸n anafor¸n, 
diˆdoshc gn¸shc, koinwnik c epirro c, koin¸n asqoli¸n, 
epanalambanìmenwn sunhjei¸n, ìpwc qr shc narkwtik¸n, klp., 
metˆdoshc [contagion] asjenei¸n k.ˆ.   diˆqushc i¸n k.ˆ. klp.). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Qarakthristikˆ Dr¸ntwn kai Diadrˆsewn 
Diaforetikèc kathgorÐec (  tÔpoi) dr¸ntwn   diadrˆsewn mporoÔn 
na enopoihjoÔn se omˆdec, stic opoÐec orÐzetai èna qarakthristikì 
(attribute), pou paÐrnei diaforetikèc timèc se kˆje omˆda. 
Genik¸c, kˆje qarakthristikì mporeÐ na jewrhjeÐ wc mia metablht , 
eÐte posotik  (suneq¸n   diakrit¸n tim¸n)   poiotik  (diataktik¸n 
[ordinal]   onomastik¸n] [nominal] tim¸n). P.q.: 
'Arrenec kai j leic dr¸ntec omadopoioÔntai kˆtw apì to 
(poiotikì) onomastikì qarakthristikì tou fÔlou. 
Dr¸ntec diaforetikoÔ bˆrouc omadopoioÔntai kˆtw apì to 
(posotikì) suneqèc qarakthristikì tou bˆrouc. 
Diadrˆseic hlektronik c epikoinwnÐac omadopoioÔntai kˆtw apì 
to (posotikì) diakritì qarakthristikì tou pl jouc   thc 
suqnìthtac twn antallassìmenwn mhnumˆtwn (se kˆpoia 
perÐodo). 
Diadrˆseic diaforetik¸n bajm¸n thc sqèshc filÐac omadopoioÔ- 
ntai kˆtw apì to (poiotikì) diataktikì qarakthristikì thc 
diabˆjmishc thc èntashc thc sqèshc filÐac. 
Diadrˆseic sumpˆjeiac–antipˆjeiac omadopoioÔntai kˆtw apì 
to (poiotikì) diataktikì (duadikì) qarakthristikì tou 
prìshmou (jetikoÔ   arnhtikoÔ) thc sqèshc. 
Oi antÐstoiqoi grˆfoi eÐnai oi grˆfoi me bˆrh   (timèc) (weighted– 
valued graphs) stouc kìmbouc   stouc sundèsmouc. Eidikˆ sto teleu- 
taÐo parˆdeigma, onomˆzontai proshmasmènoi grˆfoi (signed graphs). 
'Ena dÐktuo, sto opoÐo oi Ðdioi dr¸ntec diathroÔn perissìterec thc 
miac diaforetikèc diadrˆseic onomˆzetai polusqidèc (multiplex). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Diktuakèc AnalÔseic 
1 Koinwnikˆ Diktuakˆ Dedomèna 
Erwthmatolìgia kai sunenteÔxeic 
Istorikˆ arqeÐa kai arqeÐa tÔpou 
Bibliometrikˆ kai episthmometrikˆ dedomèna 
Dedomèna apì to Internet (mhnÔmata, istoselÐdec, 
mplogk, koinwnikˆ mèsa) 
Sqesiakˆ Megˆla Dedomèna (Big Data) kai Anoiktˆ 
Dedomèna (Open Data) 
2 Diktuakˆ Mètra 
BajmoÐ kìmbwn – Istogrˆmmata 
Kentrikìthtec kìmbwn 
Suntelest c suss¸reushc kai metabatikìthta 
Amoibaiìthta sundèsmwn 
Apostˆseic kìmbwn 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
3 DiktuakoÐ diamerismoÐ 
Sunektikèc sunist¸sec kai klÐkec 
k–pur nec 
Pur nac–perifèreia 
IsodunamÐec kìmbwn (domik  kai kanonik ) 
OmadopoÐhsh se mplok Blockmodeling 
Koinìthtec (Communities) 
Taxinomhsimìthta (assortativity) kai anˆmeixh (mixing) 
4 Qronik¸c Exart¸mena DÐktua 
Troqièc metabˆsewn 
5 Statistik  JewrÐa DiktÔwn 
Exponential Random Graph Models (ERGM) 
6 Montelopoi seic DiktÔwn 
Koinwnik  epirro  
Diˆqush (montèla SIR kai SIS) 
TuqaÐoi grˆfoi Erd¨os–Re´ nyi 
DÐktua mikr¸n kìsmwn (small–worlds) 
DÐktua qwrÐc klÐmaka (scale–free) 
Auxanìmena tuqaÐa dÐktua kai to montèlo 
Bara´ basi–Albert 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Mia Panoramik  'Ekjesh Diktuak¸n 
'Ergwn 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
To DÐktuo twn Flwrentian¸n OÐkwn 
Sq ma: To dÐktuo twn gˆmwn metaxÔ twn megˆlwn OÐkwn thc 
FlwrentÐac tou mesaÐwna (Padgett & Ansell, Robust action and the rise of the 
Medici, 1400–1434, American Journal of Sociology, 1993, 98(6): 1259­1319). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
To DÐktuo twn Sten¸n Sunergat¸n tou Santˆm 
Sq ma: To dÐktuo tou eswterikoÔ kÔklou twn sten¸n sunergat¸n tou 
Santˆm Qouseòn (Baraba´ si et al., Network Science Book, 
http://barabasilab.neu.edu/networksciencebook/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo FilÐac Mel¸n Lèsqhc Karˆte 
Sq ma: DÐktuo filÐac twn 34 mel¸n miac Panepisthmiak c lèsqhc karˆte 
(Zachary, An information flow model for conflict and fission in small groups, 
Journal of Anthropological Research, 1977, 33: 452­473). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Sunaisjhmatik¸n Sqèsewn 
Sq ma: DÐktuo sunaisjhmatik¸n–erwtik¸n sqèsewn (Bearman et al., 
Chains of affection: The structure of adolescent romantic and sexual networks, 
American Journal of Sociology, 2004, 110: 44­91) 
se optikopoÐhsh tou Mark 
Newman (http://www-personal.umich.edu/~mejn/networks/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
To dÐktuo twn AjlÐwn tou BÐktwroc Ougk¸ 
Sq ma: To dÐktuo twn sqèsewn metaxÔ twn kÔriwn qarakt rwn twn 
AjlÐwn tou BÐktwroc Ougk¸ (ta qr¸mata antistoiqoÔn se koinìthtec, pou 
upologÐsjhkan ek twn ustèrwn) (Newman & Girvan, Finding and evaluating 
community structure in networks, Physical Review E, 2004, 69: 026113). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
KuriarqoÔntec kìmboi kai koinìthtec sto 
dÐktuo twn AjlÐwn 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo PaqÔsarkwn Atìmwn 
Sq ma: DÐktuo paqÔsarkwn atìmwn (Christakis & Fowler, The spread of 
obesity in a large social network over 32 years, New Englnd Journal of Medicine, 
2007, 357(4): 370­379) 
[Mègejoc kìmbwn BMI, kÐtrinoi paqÔsarkoi, 
prˆsino mh paqÔsarkoi, mwb sundèseic filÐa, portokalÐ suggeneÐc.] 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Eutuqismènwn Atìmwn 
Sq ma: DÐktuo eutuqismènwn atìmwn (Fowler & Christakis, Dynamic spread 
of happiness in a large social network: Longitudinal analysis over 20 years in the 
Framingham Heart Study, British Medical Journal, 2008, 337(768): a2338). 
Kìmboi tetragwnikoÐ gunaÐkec, kuklikoÐ ˆndrec, mple ligìtero eutuqeÐc, 
kÐtrino perissìtero eutuqeÐc, kìkkinec sundèseic filÐa, maÔrec suggeneÐc.] 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo FilÐac Majht¸n tou Faux Magnolia High School 
Sq ma: To dÐktuo filÐac 1461 majht¸n tou Faux Magnolia High School 
qwrÐc apomonwmènouc kìmbouc (Goudreau et al., A statnet Tutorial, Journal of 
Statistical Software, 2008, 24(9): 1­27). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo FilÐac Majht¸n tou Faux Magnolia High School me to 
Qarakthristikì tou 'Etouc FoÐthshc twn Majht¸n 
Sq ma: To dÐktuo filÐac 1461 majht¸n tou Faux Magnolia High School me 
to qarakthristikì tou ètouc foÐthshc twn majht¸n kai qwrÐc 
apomonwmènouc kìmbouc (Goudreau et al., A statnet Tutorial, Journal of 
Statistical Software, 2008, 24(9): 1­27). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo FilÐac me to Qarakthristikì thc Ful c twn Majht¸n 
Sq ma: 'Ena dÐktuo filÐac majht¸n me to qarakthristikì thc ful c twn majht¸n (kÐtrino = 
leukoÐ, prˆsino = maÔroi, kìkkino = ˆllhc ful c) kai qwrÐc apomonwmènouc kìmbouc (Moody, Race, 
school integration, and friendship segregation in America, American Journal of Sociology, 2001, 107: 
679­716) 
se optikopoÐhsh tou Mark Newman (http://www-personal.umich.edu/~mejn/networks/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo SunergasÐac sthn Santa Fe 
Sq ma: DÐktuo sunergasÐac episthmìnwn tou InstitoÔtou Santa Fe (Girvan 
& Newman, Community structure in social and biological networks, Proceedings of 
the National Academy of Sciences of the USA, 2002, 99: 8271­8276). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Parapomp¸n sthn KoinwniologÐa 
Sq ma: DÐktuo bibliografik¸n parapomp¸n sthn KoinwniologÐa apì dedomèna tou Jim Moody 
(http://orgtheory.wordpress.com/2009/08/14/sociologys-citation-core/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
To DÐktuo twn Qwr¸n me Megˆlo Qrèoc 
Sq ma: To dÐktuo twn qwr¸n me megˆla qrèh (Baraba´ si et al., Network 
Science Book, http://barabasilab.neu.edu/networksciencebook/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Trofikìc Istìc tou Oikosust matoc miac LÐmnhc 
Sq ma: To dÐktuo tou trofikoÔ istoÔ (food web) tou oikosust matoc thc 
LÐmnhc Little Rock tou Wisconsin (Martinez, Artifacts or attributes? Effects of 
resolution on the Little Rock Lake food web, Ecological Monographs, 1991, 61: 
367­392). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Fainotupik¸n Asjenei¸n 
Sq ma: DÐktuo fainotupik¸n asjenei¸n (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). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
To Internet 
Sq ma: To dÐktuo twn ISPs tou Internet (Cheswick & Burch, Internet Atlas Gallery, 
http://www.caida.org/projects/internetatlas/gallery/ches/data.xml). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
To Facebook 
Sq ma: To dÐktuo epikoinwnÐac tou Facebook (Baraba´ si et al., Network 
Science Book, http://barabasilab.neu.edu/networksciencebook/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Twitter 
Sq ma: H gigantiaÐa sunektik  sunist¸sa enìc diktÔou Twitter gia 
kˆpoia RTs (retweets) pou èginan anaforikˆ me ta gegonìta diamarturÐac 
sthn TourkÐa ton IoÔnio tou 2013. 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo LinkedIn 
Sq ma: Oi koinoÐ – moirasmènoi (shared) – fÐloi gia duo qr stec tou 
LinkedIn. 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo (Dia–)Kleidwmènwn DS Etairi¸n 
(Interlocking Directorates) 
Sq ma: DÐktuo (Dia–)Kleidwmènwn (Interlocking Directorates) Dioikhtik¸n SumboulÐwn Etairi¸n 
apì koinèc summetoqèc steleq¸n se autèc 
(http://orgtheory.wordpress.com/2011/08/19/theyrule-net-interlocking-boards/, 
http://theyrule.net/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
To DÐktuo BioteqnologÐac–BiomhqanÐac stic 
HPA 
Sq ma: To dÐktuo twn sqèsewn BioteqnologÐac–BiomhqanÐac stic HPA (Powell, White, Koput & 
Owen–Smith, Network Dynamics and Field Evolution: The Growth of Interorganizational Collaboration in the 
Life Sciences, American Journal of Sociology, 2005, 110(4): 1132­1205, 
http://eclectic.ss.uci.edu/~drwhite/Movie/). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Summetoq¸n se Koinwnikèc Ekdhl¸seic 
Gunaik¸n tou Nìtou 
Sq ma: DÐktuo summetoq¸n–maz¸xewn se 14 sumbˆnta koinwnik¸n 
ekdhl¸sewn 18 gunaik¸n tou Amerikˆnikou Nìtou (Davis, Gardner & Gardner, 
Deep Douth, University of Chicago Press, 1941). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Yhfofori¸n sto An¸tero Dikast rio 
twn HPA 
Sq ma: DÐktuo yhfofori¸n sto An¸tero Dikast rio twn HPA me tic suneqìmenec grammèc na 
sumbolÐzoun jetikèc y fouc kai tic diakoptìmenec grammèc arnhtikèc y fouc (Mrvar & Doreian, 
Partitioning signed two­mode 
networks, Journal of Mathematical Sociology, 2009, 33: 196­221). 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
DÐktuo Epitrop¸n sthn Boul  twn 
Antipros¸pwn twn ARTICLE HPA 
IN PRESS 
BUDGET 
VETERANS’ AFFAIRS 
ARMED SERVICES 
AGRICULTURE 
420 M.A. Porter et al. / Physica A 386 (2007) 414–438 
APPROPRIATIONS 
INTELLIGENCE 
HOUSE ADMINISTRATION 
ENERGY/COMMERCE 
OFFICIAL CONDUCT 
HOMELAND SECURITY 
GOVERNMENT REFORM 
WAYS AND MEANS 
INTERNATIONAL RELATIONS 
TRANSPORTATION 
SMALL BUSINESS 
EDUCATION 
SCIENCE 
FINANCIAL SERVICES 
RULES 
RESOURCES 
JUDICIARY 
Sq ma: Fig. 4. (Color) Network of committees (squares) and subcommittees (circles) in the 108th US House of Representatives, color-coded by 
the DÐktuo parent standing epitrop¸n and select committees. (tetrˆgwna(The depicted ) labels kai indicate upo–the epitrop¸n parent committee (of kÔkloieach group ) sthn but do not 108identify h Boul  the 
twn 
Antipros¸pwn 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 Kamada–Kawai spring 
embedder, with link strengths (again indicated by darkness) determined by normalized interlocks. Observe structure again that subcommittees in the United of the 
States 
House of Representatives, same parent committee Physica are closely A, connected 2007, to each 386: other. 
414­438). 
Oi sundèseic anaparistoÔn koinèc 
summetoqèc bouleut¸n se (upo)epitropèc. 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn 
Security Committee shares only one common member (normalized interlock 2.4) with the Intelligence Select 
Committee (located near the 1 o’clock position in Fig. 5) and has no interlock at all with any of the four
LÐga Endeiktikˆ ParadeÐgmata 
Diktuak¸n Upologism¸n 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
BasikoÐ SumbolismoÐ JewrÐac Grˆfwn 
'Enac grˆfoc G eÐnai èna zeÔgoc (V, E), ìpou to V eÐnai 
èna sÔnolo koruf¸n (  kìmbwn   shmeÐwn) kai to E 
eÐnai èna sÔnolo akm¸n (  gramm¸n   sundèsmwn   
sundèsewn). 
'Etsi, o grˆfoc grˆfetai wc G = (V, E) ki, ìtan qreiˆzetai na epishmˆnoume 
ìti to V eÐnai to sÔnolo koruf¸n tou grˆfou G, grˆfoume V = V(G) kai, 
parìmoia, ìti to E eÐnai to sÔnolo akm¸n tou G, grˆfoume E = E(G). 
Kˆje akm  e 2 E enìc grˆfou G = (V, E) antistoiqeÐ se duo korufèc tou 
sunìlou V, oi opoÐec apoteloÔn ta duo ˆkra thc akm c. 'Otan ta ˆkra thc 
akm c e 2 E eÐnai oi korufèc u kai v 2 V, grˆfoume e = (u, v). Shmeiwtèon ìti 
oi akmèc den èqoun kateÔjunsh, dhlad , e = (u, v) = (v, u). 
O grˆfoc 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 2 
v1  
v2 ❅ 
❅ 
v4  
v3 
❅ 
❅ 
V = {v1, Mwus c v2, Av3}, . MpountourÐdhc E = {{v3, H Epist mh v4}, {v2, twn v3}, DiktÔwn 
{v1, v3}}
observe that G1 ⊕ G2 = G1 ∪ G2. However, usually for ring sums we have the same vertex 
TÔpoi Grˆfwn 
= 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 brìqoc (loop) eÐnai mia akm  pou en¸nei mia koruf  v me ton 
eautì thc, e = (v, v). 
Duo (  perissìterec) akmèc onomˆzontai parˆllhlec an ta ˆkra touc 
eÐnai oi Ðdiec korufèc. 
'Enac grˆfoc qwrÐc brìqouc kai qwrÐc parˆllhlec akmèc onomˆzetai 
aplìc, en¸ diaforetikˆ onomˆzetai pollaplìc grˆfoc (multi–graph). 
'Enac grˆfoc onomˆzetai grˆfoc me bˆrh (weighted graph) kai 
sumbolÐzetai wc G = (V, E,w), an se kˆje akm  tou e antistoiqeÐ èna 
bˆroc   mia tim  w(e) 2 R. 
Directed Graphs 
Definition 10 
directed 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 kateujunìmenoc grˆfoc   digrˆfoc G eÐnai èna zeÔgoc (V, E), ìpou to 
V eÐnai èna sÔnolo koruf¸n (  kìmbwn   shmeÐwn) kai to E eÐnai èna 
sÔnolo tìxwn me to kˆje tìxo e 2 E na antistoiqeÐ se èna diatetagmèno 
zeÔgoc koruf¸n (u, v) ètsi ¸ste na kateujÔnetai apì thn koruf  u proc 
thn koruf  v. 
O kateujunìmenoc grˆfoc 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 associated 
with the edge e they are called the endpoints of e, we often write uv or (u, v) to represent the 
arc e. 
Example 11 
v1  
❅ ✻ 
❅ 
v4  
v2 
v3 
❅ 
❅❘ 
✲ 
V Mwus c = {v1, A. v2, MpountourÐdhc v3}, E = {(v4, H v3), Epist mh (v3, twn v2), DiktÔwn 
(v1, v3)}
DimereÐc Grˆfoi 
'Enac grˆfoc onomˆzetai dimer c 
(bipartite), ìtan upˆrqei ènac 
diamerismìc tou sunìlou twn 
koruf¸n tou V se duo mèrh 
(tm mata), to U kai to W, dhlad , 
V = U [W (ìpou U W = ?), ètsi 
¸ste ìlec oi akmèc na phgaÐnoun 
apì to U sto W kai na mhn 
upˆrqei kamiˆ akm  oÔte metaxÔ 
koruf¸n tou U oÔte metaxÔ 
koruf¸n tou W. 
Probolèc dimeroÔc grˆfou: 
u1 
u3 
u2 
u4 
u1 
u2 
u3 
u4 
w1 
w2 
w3 w2 
w1 
w3 
1 
2 
2 
1 
1 2 
1 
2 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
BajmoÐ Kìmbwn 
GeÐtonec: 'Estw o mh kateujunìmenoc grˆfoc G = (V, E) kai i, j 2 V 
duo korufèc tou. H j lègetai geÐtonac thc i ìtan (i, j) 2 E. 
PÐnakac GeitnÐashc (Adjacency Matrix): EÐnai ènac 
(summetrikìc) pÐnakac A = fAgi,j2V tˆxhc jVj  jVj tètoioc ¸ste 
A = 1, ìtan i, j geÐtonec, A = 0, diaforetikˆ. 
BajmoÐ: Sto mh kateujunìmeno grˆfo G, o bajmìc miac koruf c i, 
pou sumbolÐzetai wc ki, orÐzetai san to pl joc twn geitìnwn tou i, 
dhlad , to pl joc twn sundèsewn pou prospÐptoun sto i. 
Profan¸c, isqÔei: 
ki = 
X 
j2V 
A = 
X 
i2V 
A 
ki, epiplèon, 
X 
i2V 
ki = 
X 
i,j2V 
A = 2jEj 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
'Estw t¸ra o kateujunìmenoc grˆfoc G = (V, E), gia ton opoÐon o 
antÐstoiqoc pÐnakac geitnÐashc A = fAg eÐnai mh summetrikìc. 
O bajmìc eisìdou thc koruf c i tou G, pou sumbolÐzetai wc kin i , 
orÐzetai san to pl joc twn sundèsewn pou xekinoÔn apì geÐtonec 
tou i kai kateujÔnontai proc ton i, dhlad , 
kin 
i = 
X 
j2V 
A 
O bajmìc exìdou thc koruf c i tou G, pou sumbolÐzetai wc kout i , 
orÐzetai san to pl joc twn sundèsewn pou xekinoÔn apì ton i kai 
kateujÔnontai proc geÐtonec tou i, dhlad , 
kout 
i = 
X 
i2V 
A 
Profan¸c, isqÔei: 
X 
i2V 
kin 
i = 
X 
j2V 
kout 
i = 
X 
i,j2V 
A = jEj 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
BajmoÐ kìmbwn sto dÐktuo karˆte 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
GenikoÐ TÔpoi Diktuak¸n Katanom¸n Bajm¸n 
Sq ma: Diwnumik  Katanom  (  Katano- 
m  Poisson) gia tuqaÐouc grˆfouc Erd¨os–Re´ nyi 
Sq ma: Katanom  Nìmou DÔnamhc (Power 
Law) gia dÐktua qwrÐc klÐmaka (scale–free 
networks) 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Kentrikìthtec Kìmbwn: 
1. Kentrikìthta BajmoÔ (Degree Centrality) 
Oi orismoÐ OLWN twn kentrikìthtwn pou ja d¸soume 
ed¸ kai sth sunèqeia aforoÔn mh kateujunìmenouc 
(aploÔc) grˆfouc. 
H kentrikìthta bajmoÔ (degree centrality) xi tou kìmbou 
i isoÔtai proc ton bajmì ki tou kìmbou autoÔ: 
xi = ki 
x8 = 5 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
2. Kentrikìthta Endiamesìthtac 
(Betweenness Centrality) 
H kentrikìthta endiamesìthtac (betweenness centrality) xi tou kìmbou 
i isoÔtai proc: 
xi = 
X 
s6=i6=t2V 
nist 
gst 
ìpou nist eÐnai to pl joc twn gewdaitik¸n diadrom¸n metaxÔ twn 
kìmbwn s kai t, pou pernoÔn apì ton kìmbo i, kai gst eÐnai to sunolikì 
pl joc twn gewdaitik¸n diadrom¸n metaxÔ twn kìmbwn s kai t. 
n23 
,23 = 2 
g3,23 = 4 
x2 = 0.1436 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
3. Kentrikìthta EggÔthtac 
(Closeness Centrality) 
Se ènan grˆfo G, gia kˆje duo kìmbouc i, j, h (gewdaitik ) apìstas  
touc d(i, j) orÐzetai wc to m koc thc suntomìterhc diadrom c apì to i 
sto j, efìson oi kìmboi autoÐ eÐnai sundedemènoi, en¸ d(i, j) = 1, 
diaforetikˆ (kai fusikˆ, d(i, i) = 0). (H ‘‘suntomìterh diadrom ’’ 
metaxÔ duo kìmbwn eÐnai h diadrom  pou èqei to elˆqisto m koc 
anˆmesa se ìlec tic diadromèc metaxÔ twn duo kìmbwn.) 
Se ènan grˆfo me n kìmbouc, h kentrikìthta eggÔthtac (closeness 
centrality) xi tou kìmbou i isoÔtai proc: 
xi = 
n P 
j2V d(i, j) 
x0 = 0.5689 
x2 = 0.5593 
x33 = 0.55 
x31 = 0.5409 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
4. Kentrikìthta IdiodianÔsmatoc 
(Eigenvector Centrality) 
H kentrikìthta idiodianÔsmatoc (eigenvector centrality) xi tou kìmbou i 
isoÔtai proc: 
xi = 1 
1 
X 
j2V 
Axj 
ìpou A eÐnai o pÐnakac geitnÐashc (adjacency matrix) tou grˆfou kai 
xi eÐnai oi sunist¸sec tou idiadianÔsmatoc tou A, pou antistoiqoÔn 
sth megalÔterh idiotim  tou 1. 
x33 = 0.3734 
x0 = 0.3555 
x2 = 0.3172 
x32 = 0.3086 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Oi 4 kentrikìthtec twn kìmbwn tou diktÔou karˆte 
Nodes Degree C. Betweenness C. Closeness C. Eigenvector C. 
0 0.484848485 0.437635281 0.568965517 0.355490721 
1 0.272727273 0.053936688 0.485294118 0.265959605 
2 0.303030303 0.143656806 0.559322034 0.317192417 
3 0.181818182 0.011909271 0.464788732 0.211179694 
4 0.090909091 0.000631313 0.379310345 0.075968879 
5 0.121212121 0.029987374 0.38372093 0.079483113 
6 0.121212121 0.029987374 0.38372093 0.079483113 
7 0.121212121 0 0.44 0.170959892 
8 0.151515152 0.055926828 0.515625 0.227404355 
9 0.060606061 0.000847763 0.434210526 0.102674504 
10 0.090909091 0.000631313 0.379310345 0.075968879 
11 0.03030303 0 0.366666667 0.052855817 
12 0.060606061 0 0.370786517 0.084254727 
13 0.151515152 0.045863396 0.515625 0.226473112 
14 0.060606061 0 0.370786517 0.10140365 
15 0.060606061 0 0.370786517 0.10140365 
16 0.060606061 0 0.284482759 0.023635566 
17 0.060606061 0 0.375 0.092399699 
18 0.060606061 0 0.370786517 0.10140365 
19 0.090909091 0.032475048 0.5 0.147912918 
20 0.060606061 0 0.370786517 0.10140365 
21 0.060606061 0 0.375 0.092399699 
22 0.060606061 0 0.370786517 0.10140365 
23 0.151515152 0.017613636 0.392857143 0.150118912 
24 0.090909091 0.002209596 0.375 0.057052326 
25 0.090909091 0.003840488 0.375 0.059206342 
26 0.060606061 0 0.362637363 0.075579616 
27 0.121212121 0.022333454 0.458333333 0.133477386 
28 0.090909091 0.001794733 0.452054795 0.131077964 
29 0.121212121 0.002922078 0.38372093 0.134961122 
30 0.121212121 0.014411977 0.458333333 0.174758637 
31 0.181818182 0.138275613 0.540983607 0.191034394 
32 0.363636364 0.145247114 0.515625 0.308643749 
33 0.515151515 0.304074976 0.55 0.373362539 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Kentrikìthta Mikr  tim  Megˆlh tim  
Degree LÐgoi geÐtonec (sundèseic) PolloÐ geÐtonec (sundèseic) 
Betweenness Mikrìc èlegqoc ro c Megˆloc èlegqoc ro c 
Closeness Proc thn perifèreia Proc to kèntro 
Eigenvector LÐgoi   lÐgo shmantikoÐ geÐtonec PolloÐ   polÔ shmantikoÐ geÐtonec 
To dÐktuo twn stratiwtik¸n tou David Krackhardt: 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Suntelest c Suss¸reushc 
O suntelest c suss¸reushc (clustering coefficient) Ci tou kìmbou i 
orÐzetai wc: 
Ci = 
2i 
ki(ki  1) 
ìpou i eÐnai to pl joc twn sundèsewn metaxÔ twn geitonik¸n 
kìmbwn tou i kai d i proc opoiod pote ˆllo kìmbo ki eÐnai to 
pl joc twn geitonik¸n kìmbwn tou i. 
C23 = 
2  4 
5  4 = 0.4 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Diktuak  Metabatikìthta 
O sunolikìc suntelest c suss¸reushc (global clustering coefficient) 
(ìlou) tou grˆfou G orÐzetai wc h mèsh tim  twn suntelest¸n 
suss¸reushc twn kìmbwn tou: 
C(G) = 
1 
jVj 
X 
i 
Ci 
H metabatikìthta (transitivity) tou grˆfou G orÐzetai wc to phlÐko: 
T(G) = 
pl joc trig¸nwn 
pl joc sundedemènwn triˆdwn 
C(G) = 0.16 
T(G) = 0.19 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Amoibaiìthta Sundèsewn se Kateujunìmeno Grˆfo 
Se ènan kateujunìmeno grˆfo, o suntelest c amoibaiìthtac 
sundèsewn/desm¸n (link/tie mutuality coefficient) orÐzetai wc ex c: 
M(G) = 
pl joc antapodidìmenwn sundèsewn Er 
pl joc ìlwn twn sundèsewn/tìxwn E 
Er(G) = 64 
E(G) = 195 
M(G) = 0.3282 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Apostˆseic Kìmbwn se Grˆfo 
SumbolÐzontac me d(i, j) th (gewdaitik ) apìstash ston grˆfo G 
metaxÔ twn duo kìmbwn i, j (dhlad , wc m koc thc suntomìterhc 
diadrom c apì to i sto j, efìson oi kìmboi autoÐ eÐnai sundedemènoi, 
en¸ d(i, j) = 1, ìpou h ‘‘suntomìterh diadrom ’’ metaxÔ duo kìmbwn 
eÐnai h diadrom  pou èqei to elˆqisto m koc anˆmesa se ìlec tic 
diadromèc metaxÔ twn duo kìmbwn), to mèso m koc twn suntomìterwn 
diadrom¸n (average shortest path length) ston grˆfo autì, orÐzetai wc: 
a = 
1 
jVj(jVj  1) 
X 
i,j2V 
d(i, j) 
a = 2.4082 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Mètra Diˆforwn Empeirik¸n DiktÔwn TABLE I. The general characteristics of several real networks. For each network we indicated the number of nodes, the average 
degree !k, the average path length ! and the clustering coefficient C. For a comparison we have included the average path 
length !rand and clustering coefficient Crand of a random graph with the same size and average degree. The last column 
identifies the symbols in Figs. 8 and 9. 
Network Size !k ! !rand C Crand Reference Nr. 
WWW, site level, undir. 153, 127 35.21 3.1 3.35 0.1078 0.00023 Adamic 1999 Internet, domain level 3015 - 6209 3.52 - 4.11 3.7 - 3.76 6.36 - 6.18 0.18 - 0.3 0.001 Yook et al. 2001a, 
Pastor-Satorras et al. 2001 Movie actors 225, 226 61 3.65 2.99 0.79 0.00027 Watts, Strogatz 1998 LANL coauthorship 52, 909 9.7 5.9 4.79 0.43 1.8 × 10−4 Newman 2001a,b MEDLINE coauthorship 1, 520, 251 18.1 4.6 4.91 0.066 1.1 × 10−5 Newman 2001a,b SPIRES coauthorship 56, 627 173 4.0 2.12 0.726 0.003 Newman 2001a,b,c NCSTRL coauthorship 11, 994 3.59 9.7 7.34 0.496 3 × 10−4 Newman 2001a,b Math coauthorship 70, 975 3.9 9.5 8.2 0.59 5.4 × 10−5 Barab´asi et al. 2001 Neurosci. coauthorship 209, 293 11.5 6 5.01 0.76 5.5 × 10−5 Barab´asi et al. 2001 E. coli, substrate graph 282 7.35 2.9 3.04 0.32 0.026 Wagner, Fell 2000 10 
E. coli, reaction graph 315 28.3 2.62 1.98 0.59 0.09 Wagner, Fell 2000 11 
Ythan estuary food web 134 8.7 2.43 2.26 0.22 0.06 Montoya, Sol´e 2000 12 
Silwood park food web 154 4.75 3.40 3.23 0.15 0.03 Montoya, Sol´e 2000 13 
Words, cooccurence 460.902 70.13 2.67 3.03 0.437 0.0001 Cancho, Sol´e 2001 14 
Words, synonyms 22, 311 13.48 4.5 3.84 0.7 0.0006 Yook et al. 2001 15 
Power grid 4, 941 2.67 18.7 12.4 0.08 0.005 Watts, Strogatz 1998 16 
C. Elegans 282 14 2.65 2.25 0.28 0.05 Watts, Strogatz 1998 17 
TABLE II. The scaling exponents characterizing the degree distribution of several scale-free networks, for which P(k) follows 
a power-law (2). We indicate the size of the network, its average degree !k and the cutoff  for the power-law scaling. For 
directed networks we list separately the indegree (#in) and outdegree (#out) exponents, while for the undirected networks, 
marked with a star, these values are identical. The columns lreal , lrand and lpow compare the average path length of real 
networks with power-law degree distribution and the prediction of random graph theory (17) and that of Newman, Strogatz 
and Watts (2000) (62), as discussed in Sect. V. The last column identifies the symbols in Figs. 8 and 9. 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
EndeiktikoÐ Pìroi 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
Pìroi gia Eisagwg  sta Koinwnikˆ DÐktua 
1 BiblÐa 
Mark Newman, Networks: An Introduction, Oxford 
University Press, 2010. 
Stanley Wasserman and Katherine Faust, Social Network 
Analysis: Methods and Applications, Cambridge 
University Press, 1994. 
2 'Arjra Episkìphshc 
Mark Newman, The structure and function of complex 
networks: http://arxiv.org/pdf/cond-mat/0303516v1 
Laszlo Bara´ basi et al., Network Science Book: 
http://barabasilab.neu.edu/networksciencebook/ 
Robert A. Hanneman and Mark Riddle, Introduction to 
social network methods: 
http://faculty.ucr.edu/~hanneman/nettext/ 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
3 Logismikì 
NetworkX: http://networkx.github.io/ 
Gephi: http://gephi.github.io/ 
Pajek: http://pajek.imfm.si/doku.php 
UCInet: 
https://sites.google.com/site/ucinetsoftware/home 
iGraph: http://igraph.sourceforge.net/ 
Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn

Contenu connexe

En vedette

Goo Create: Import animation
Goo Create: Import animationGoo Create: Import animation
Goo Create: Import animationGoo Technologies
 
Art 2100 Online syllabus summer i 2016
Art 2100 Online syllabus summer i 2016Art 2100 Online syllabus summer i 2016
Art 2100 Online syllabus summer i 2016Lydia Dorsey
 
The natural leadership talents of women
The natural leadership talents of womenThe natural leadership talents of women
The natural leadership talents of womenKenia Alvarez-Tio
 
Goo Create: Interface Overview
Goo Create: Interface OverviewGoo Create: Interface Overview
Goo Create: Interface OverviewGoo Technologies
 
Dye living room furniture selections
Dye living room furniture selectionsDye living room furniture selections
Dye living room furniture selectionsErica Peale
 
Dye family room furniture selections
Dye family room furniture selectionsDye family room furniture selections
Dye family room furniture selectionsErica Peale
 
Dold Chris Ignite Slideshow
Dold Chris Ignite SlideshowDold Chris Ignite Slideshow
Dold Chris Ignite Slideshowchrisdold
 

En vedette (12)

Goo Create: Import animation
Goo Create: Import animationGoo Create: Import animation
Goo Create: Import animation
 
Art 2100 Online syllabus summer i 2016
Art 2100 Online syllabus summer i 2016Art 2100 Online syllabus summer i 2016
Art 2100 Online syllabus summer i 2016
 
The natural leadership talents of women
The natural leadership talents of womenThe natural leadership talents of women
The natural leadership talents of women
 
Physical activity
Physical  activityPhysical  activity
Physical activity
 
Karthik
KarthikKarthik
Karthik
 
Goo Create: Interface Overview
Goo Create: Interface OverviewGoo Create: Interface Overview
Goo Create: Interface Overview
 
Dye living room furniture selections
Dye living room furniture selectionsDye living room furniture selections
Dye living room furniture selections
 
French vocab rehab
French vocab rehabFrench vocab rehab
French vocab rehab
 
Fotografías
FotografíasFotografías
Fotografías
 
Dye family room furniture selections
Dye family room furniture selectionsDye family room furniture selections
Dye family room furniture selections
 
Dold Chris Ignite Slideshow
Dold Chris Ignite SlideshowDold Chris Ignite Slideshow
Dold Chris Ignite Slideshow
 
Stmt trisakati kel.1
Stmt trisakati kel.1Stmt trisakati kel.1
Stmt trisakati kel.1
 

Similaire à Η Επιστήμη των Δικτύων: Μια Πολύ Σύντομη Εισαγωγική Παρουσίαση - 8 Οκτωβρίου 2014

Evidence-Based Practice Scoring Guide Grading RubricCriteria.docx
Evidence-Based Practice Scoring Guide Grading RubricCriteria.docxEvidence-Based Practice Scoring Guide Grading RubricCriteria.docx
Evidence-Based Practice Scoring Guide Grading RubricCriteria.docxSANSKAR20
 
Letter Of Intent Template Essay
Letter Of Intent Template EssayLetter Of Intent Template Essay
Letter Of Intent Template EssayLaura Johnson
 
PAPER 3.1 ~ HUMAN GENOME PROJECT
PAPER 3.1 ~  HUMAN GENOME PROJECTPAPER 3.1 ~  HUMAN GENOME PROJECT
PAPER 3.1 ~ HUMAN GENOME PROJECTNusrat Gulbarga
 
Genome Wide Association Studies ( Gwas ) Essay
Genome Wide Association Studies ( Gwas ) EssayGenome Wide Association Studies ( Gwas ) Essay
Genome Wide Association Studies ( Gwas ) EssayMary Gregory
 
Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...
Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...
Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...Marco Ephraïm
 
Targeting Of Host Organelles By Pathogenic Bacteri A...
Targeting Of Host Organelles By Pathogenic Bacteri A...Targeting Of Host Organelles By Pathogenic Bacteri A...
Targeting Of Host Organelles By Pathogenic Bacteri A...Lucy Castillo
 
PENSOFT ARTICLE COLLECTION ABOUT MYANMAR
PENSOFT ARTICLE COLLECTION ABOUT MYANMARPENSOFT ARTICLE COLLECTION ABOUT MYANMAR
PENSOFT ARTICLE COLLECTION ABOUT MYANMARMYO AUNG Myanmar
 
Being Philosophical about Living and Dying
Being Philosophical about Living and DyingBeing Philosophical about Living and Dying
Being Philosophical about Living and DyingThe Existential Academy
 
Integrative Genomic Analysis In Cancer Essay
Integrative Genomic Analysis In Cancer EssayIntegrative Genomic Analysis In Cancer Essay
Integrative Genomic Analysis In Cancer EssayShannon Wright
 
Color Morphism Lab Report
Color Morphism Lab ReportColor Morphism Lab Report
Color Morphism Lab ReportAlyssa Jones
 
NAMs in biomedical research
NAMs in biomedical researchNAMs in biomedical research
NAMs in biomedical researchcrovida
 
Ecology And Plant Ecology
Ecology And Plant EcologyEcology And Plant Ecology
Ecology And Plant EcologySarah Griffin
 
Knowledge Discovery And Data Mining Of Free Text Final
Knowledge Discovery And Data Mining Of Free Text FinalKnowledge Discovery And Data Mining Of Free Text Final
Knowledge Discovery And Data Mining Of Free Text Finalkdjamies
 
Monitoring Assisted Reproductive Technology ( Icmart )
Monitoring Assisted Reproductive Technology ( Icmart )Monitoring Assisted Reproductive Technology ( Icmart )
Monitoring Assisted Reproductive Technology ( Icmart )Jessica Finson
 
"Causarum Cognitio: Seeking Knowledge of Causes"
"Causarum Cognitio: Seeking Knowledge of Causes""Causarum Cognitio: Seeking Knowledge of Causes"
"Causarum Cognitio: Seeking Knowledge of Causes"diannepatricia
 

Similaire à Η Επιστήμη των Δικτύων: Μια Πολύ Σύντομη Εισαγωγική Παρουσίαση - 8 Οκτωβρίου 2014 (20)

Evidence-Based Practice Scoring Guide Grading RubricCriteria.docx
Evidence-Based Practice Scoring Guide Grading RubricCriteria.docxEvidence-Based Practice Scoring Guide Grading RubricCriteria.docx
Evidence-Based Practice Scoring Guide Grading RubricCriteria.docx
 
Letter Of Intent Template Essay
Letter Of Intent Template EssayLetter Of Intent Template Essay
Letter Of Intent Template Essay
 
PAPER 3.1 ~ HUMAN GENOME PROJECT
PAPER 3.1 ~  HUMAN GENOME PROJECTPAPER 3.1 ~  HUMAN GENOME PROJECT
PAPER 3.1 ~ HUMAN GENOME PROJECT
 
Genome Wide Association Studies ( Gwas ) Essay
Genome Wide Association Studies ( Gwas ) EssayGenome Wide Association Studies ( Gwas ) Essay
Genome Wide Association Studies ( Gwas ) Essay
 
Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...
Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...
Anthroposophic Medicine 2013. An Integrative Medical System Originating in Eu...
 
Targeting Of Host Organelles By Pathogenic Bacteri A...
Targeting Of Host Organelles By Pathogenic Bacteri A...Targeting Of Host Organelles By Pathogenic Bacteri A...
Targeting Of Host Organelles By Pathogenic Bacteri A...
 
PENSOFT ARTICLE COLLECTION ABOUT MYANMAR
PENSOFT ARTICLE COLLECTION ABOUT MYANMARPENSOFT ARTICLE COLLECTION ABOUT MYANMAR
PENSOFT ARTICLE COLLECTION ABOUT MYANMAR
 
Human genome project 1
Human genome project 1Human genome project 1
Human genome project 1
 
Being Philosophical about Living and Dying
Being Philosophical about Living and DyingBeing Philosophical about Living and Dying
Being Philosophical about Living and Dying
 
Integrative Genomic Analysis In Cancer Essay
Integrative Genomic Analysis In Cancer EssayIntegrative Genomic Analysis In Cancer Essay
Integrative Genomic Analysis In Cancer Essay
 
Color Morphism Lab Report
Color Morphism Lab ReportColor Morphism Lab Report
Color Morphism Lab Report
 
NAMs in biomedical research
NAMs in biomedical researchNAMs in biomedical research
NAMs in biomedical research
 
Human Genome Project
Human Genome ProjectHuman Genome Project
Human Genome Project
 
Ecology And Plant Ecology
Ecology And Plant EcologyEcology And Plant Ecology
Ecology And Plant Ecology
 
Essay On Forensic Science
Essay On Forensic ScienceEssay On Forensic Science
Essay On Forensic Science
 
Psy 435
Psy 435Psy 435
Psy 435
 
Knowledge Discovery And Data Mining Of Free Text Final
Knowledge Discovery And Data Mining Of Free Text FinalKnowledge Discovery And Data Mining Of Free Text Final
Knowledge Discovery And Data Mining Of Free Text Final
 
Monitoring Assisted Reproductive Technology ( Icmart )
Monitoring Assisted Reproductive Technology ( Icmart )Monitoring Assisted Reproductive Technology ( Icmart )
Monitoring Assisted Reproductive Technology ( Icmart )
 
"Causarum Cognitio: Seeking Knowledge of Causes"
"Causarum Cognitio: Seeking Knowledge of Causes""Causarum Cognitio: Seeking Knowledge of Causes"
"Causarum Cognitio: Seeking Knowledge of Causes"
 
Human Genome Project
Human Genome ProjectHuman Genome Project
Human Genome Project
 

Plus de Moses Boudourides

A bibliometric study on the literature of Open Science and Open Access. By Ts...
A bibliometric study on the literature of Open Science and Open Access. By Ts...A bibliometric study on the literature of Open Science and Open Access. By Ts...
A bibliometric study on the literature of Open Science and Open Access. By Ts...Moses Boudourides
 
Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...
Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...
Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...Moses Boudourides
 
Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...
Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...
Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...Moses Boudourides
 
Experiments of Friedkin–Johnsen Social Influence on Graphs
Experiments of Friedkin–Johnsen Social Influence on GraphsExperiments of Friedkin–Johnsen Social Influence on Graphs
Experiments of Friedkin–Johnsen Social Influence on GraphsMoses Boudourides
 
Digital, Humanities, Latour and Networks. By Moses A. Boudourides
Digital, Humanities, Latour and Networks. By Moses A. BoudouridesDigital, Humanities, Latour and Networks. By Moses A. Boudourides
Digital, Humanities, Latour and Networks. By Moses A. BoudouridesMoses Boudourides
 
Δίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική Προσέγγιση
Δίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική ΠροσέγγισηΔίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική Προσέγγιση
Δίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική ΠροσέγγισηMoses Boudourides
 
Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...
Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...
Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...Moses Boudourides
 
Topics of Complex Social Networks: Domination, Influence and Assortativity
Topics of Complex Social Networks: Domination, Influence and AssortativityTopics of Complex Social Networks: Domination, Influence and Assortativity
Topics of Complex Social Networks: Domination, Influence and AssortativityMoses Boudourides
 
Slides Δικτυακών Υπολογισμών με την Python
Slides Δικτυακών Υπολογισμών με την PythonSlides Δικτυακών Υπολογισμών με την Python
Slides Δικτυακών Υπολογισμών με την PythonMoses Boudourides
 
Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...
Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...
Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...Moses Boudourides
 
Τα Πολύ Βασικά για την Python
Τα Πολύ Βασικά για την PythonΤα Πολύ Βασικά για την Python
Τα Πολύ Βασικά για την PythonMoses Boudourides
 
Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...
Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...
Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...Moses Boudourides
 
The hidden rules and open secrets of corporate governance. Preliminary result...
The hidden rules and open secrets of corporate governance. Preliminary result...The hidden rules and open secrets of corporate governance. Preliminary result...
The hidden rules and open secrets of corporate governance. Preliminary result...Moses Boudourides
 
Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...
Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...
Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...Moses Boudourides
 
Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...
Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...
Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...Moses Boudourides
 
Διακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή ΜπουντουρίδηΔιακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή ΜπουντουρίδηMoses Boudourides
 
Διακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή ΜπουντουρίδηΔιακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή ΜπουντουρίδηMoses Boudourides
 
Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...
Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...
Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...Moses Boudourides
 
Μαθαίνοντας την R σε μια ώρα
Μαθαίνοντας την R σε μια ώραΜαθαίνοντας την R σε μια ώρα
Μαθαίνοντας την R σε μια ώραMoses Boudourides
 
Πρότζεκτ για δίκτυα του LinkedIn με την Python
Πρότζεκτ για δίκτυα του LinkedIn με την PythonΠρότζεκτ για δίκτυα του LinkedIn με την Python
Πρότζεκτ για δίκτυα του LinkedIn με την PythonMoses Boudourides
 

Plus de Moses Boudourides (20)

A bibliometric study on the literature of Open Science and Open Access. By Ts...
A bibliometric study on the literature of Open Science and Open Access. By Ts...A bibliometric study on the literature of Open Science and Open Access. By Ts...
A bibliometric study on the literature of Open Science and Open Access. By Ts...
 
Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...
Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...
Boudourides: Analysis of Bibliometric Data of Publications on “Computational ...
 
Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...
Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...
Closures and Attributes in Graphs: Shadows of (Dis)Assembled Networks. By Mos...
 
Experiments of Friedkin–Johnsen Social Influence on Graphs
Experiments of Friedkin–Johnsen Social Influence on GraphsExperiments of Friedkin–Johnsen Social Influence on Graphs
Experiments of Friedkin–Johnsen Social Influence on Graphs
 
Digital, Humanities, Latour and Networks. By Moses A. Boudourides
Digital, Humanities, Latour and Networks. By Moses A. BoudouridesDigital, Humanities, Latour and Networks. By Moses A. Boudourides
Digital, Humanities, Latour and Networks. By Moses A. Boudourides
 
Δίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική Προσέγγιση
Δίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική ΠροσέγγισηΔίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική Προσέγγιση
Δίκτυα Λογοτεχνίας: Μια Πρώτη Εισαγωγική Προσέγγιση
 
Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...
Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...
Boudourides: Risk in Social Networks: Network Influence & Selection on Minori...
 
Topics of Complex Social Networks: Domination, Influence and Assortativity
Topics of Complex Social Networks: Domination, Influence and AssortativityTopics of Complex Social Networks: Domination, Influence and Assortativity
Topics of Complex Social Networks: Domination, Influence and Assortativity
 
Slides Δικτυακών Υπολογισμών με την Python
Slides Δικτυακών Υπολογισμών με την PythonSlides Δικτυακών Υπολογισμών με την Python
Slides Δικτυακών Υπολογισμών με την Python
 
Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...
Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...
Ανάλυση Δικτύων με το NetworkX της Python: Μια προκαταρκτική (αλλά ημιτελής ω...
 
Τα Πολύ Βασικά για την Python
Τα Πολύ Βασικά για την PythonΤα Πολύ Βασικά για την Python
Τα Πολύ Βασικά για την Python
 
Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...
Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...
Short version of Dominating Sets, Multiple Egocentric Networks and Modularity...
 
The hidden rules and open secrets of corporate governance. Preliminary result...
The hidden rules and open secrets of corporate governance. Preliminary result...The hidden rules and open secrets of corporate governance. Preliminary result...
The hidden rules and open secrets of corporate governance. Preliminary result...
 
Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...
Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...
Dominating Sets, Multiple Egocentric Networks and Modularity Maximizing Clust...
 
Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...
Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...
Πανεπιστήμιο και Κοινωνία των Πολιτών: Στοιχεία & Περιπτώσεις Αποικιοποίησ...
 
Διακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή ΜπουντουρίδηΔιακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά ΙI: Εισαγωγή στη Συνδυαστική. Του Μωυσή Μπουντουρίδη
 
Διακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή ΜπουντουρίδηΔιακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή Μπουντουρίδη
Διακριτά Μαθηματικά Ι: Εισαγωγή στη Λογική. Του Μωυσή Μπουντουρίδη
 
Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...
Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...
Extended Cyclic Cellular Automata: Emulating Social Influence. By Moses A. Bo...
 
Μαθαίνοντας την R σε μια ώρα
Μαθαίνοντας την R σε μια ώραΜαθαίνοντας την R σε μια ώρα
Μαθαίνοντας την R σε μια ώρα
 
Πρότζεκτ για δίκτυα του LinkedIn με την Python
Πρότζεκτ για δίκτυα του LinkedIn με την PythonΠρότζεκτ για δίκτυα του LinkedIn με την Python
Πρότζεκτ για δίκτυα του LinkedIn με την Python
 

Dernier

VIT336 – Recommender System - Unit 3.pdf
VIT336 – Recommender System - Unit 3.pdfVIT336 – Recommender System - Unit 3.pdf
VIT336 – Recommender System - Unit 3.pdfArthyR3
 
2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...Sandy Millin
 
EDD8524 The Future of Educational Leader
EDD8524 The Future of Educational LeaderEDD8524 The Future of Educational Leader
EDD8524 The Future of Educational LeaderDr. Bruce A. Johnson
 
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in PharmacyASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in PharmacySumit Tiwari
 
AI Uses and Misuses: Academic and Workplace Applications
AI Uses and Misuses: Academic and Workplace ApplicationsAI Uses and Misuses: Academic and Workplace Applications
AI Uses and Misuses: Academic and Workplace ApplicationsStella Lee
 
AUDIENCE THEORY - PARTICIPATORY - JENKINS.pptx
AUDIENCE THEORY - PARTICIPATORY - JENKINS.pptxAUDIENCE THEORY - PARTICIPATORY - JENKINS.pptx
AUDIENCE THEORY - PARTICIPATORY - JENKINS.pptxiammrhaywood
 
ICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdfICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdfVanessa Camilleri
 
3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptx3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptxmary850239
 
3.14.24 The Selma March and the Voting Rights Act.pptx
3.14.24 The Selma March and the Voting Rights Act.pptx3.14.24 The Selma March and the Voting Rights Act.pptx
3.14.24 The Selma March and the Voting Rights Act.pptxmary850239
 
LEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudLEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudDr. Bruce A. Johnson
 
Research Methodology and Tips on Better Research
Research Methodology and Tips on Better ResearchResearch Methodology and Tips on Better Research
Research Methodology and Tips on Better ResearchRushdi Shams
 
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...Nguyen Thanh Tu Collection
 
The First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdfThe First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdfdogden2
 
3.12.24 Freedom Summer in Mississippi.pptx
3.12.24 Freedom Summer in Mississippi.pptx3.12.24 Freedom Summer in Mississippi.pptx
3.12.24 Freedom Summer in Mississippi.pptxmary850239
 
Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...
Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...
Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...gdgsurrey
 
Metabolism of lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptx
Metabolism of  lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptxMetabolism of  lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptx
Metabolism of lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptxDr. Santhosh Kumar. N
 
Pharmacology chapter No 7 full notes.pdf
Pharmacology chapter No 7 full notes.pdfPharmacology chapter No 7 full notes.pdf
Pharmacology chapter No 7 full notes.pdfSumit Tiwari
 
Quantitative research methodology and survey design
Quantitative research methodology and survey designQuantitative research methodology and survey design
Quantitative research methodology and survey designBalelaBoru
 
Plant Tissue culture., Plasticity, Totipotency, pptx
Plant Tissue culture., Plasticity, Totipotency, pptxPlant Tissue culture., Plasticity, Totipotency, pptx
Plant Tissue culture., Plasticity, Totipotency, pptxHimansu10
 

Dernier (20)

VIT336 – Recommender System - Unit 3.pdf
VIT336 – Recommender System - Unit 3.pdfVIT336 – Recommender System - Unit 3.pdf
VIT336 – Recommender System - Unit 3.pdf
 
2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...2024.03.16 How to write better quality materials for your learners ELTABB San...
2024.03.16 How to write better quality materials for your learners ELTABB San...
 
EDD8524 The Future of Educational Leader
EDD8524 The Future of Educational LeaderEDD8524 The Future of Educational Leader
EDD8524 The Future of Educational Leader
 
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in PharmacyASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
ASTRINGENTS.pdf Pharmacognosy chapter 5 diploma in Pharmacy
 
AI Uses and Misuses: Academic and Workplace Applications
AI Uses and Misuses: Academic and Workplace ApplicationsAI Uses and Misuses: Academic and Workplace Applications
AI Uses and Misuses: Academic and Workplace Applications
 
AUDIENCE THEORY - PARTICIPATORY - JENKINS.pptx
AUDIENCE THEORY - PARTICIPATORY - JENKINS.pptxAUDIENCE THEORY - PARTICIPATORY - JENKINS.pptx
AUDIENCE THEORY - PARTICIPATORY - JENKINS.pptx
 
ICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdfICS2208 Lecture4 Intelligent Interface Agents.pdf
ICS2208 Lecture4 Intelligent Interface Agents.pdf
 
ANOVA Parametric test: Biostatics and Research Methodology
ANOVA Parametric test: Biostatics and Research MethodologyANOVA Parametric test: Biostatics and Research Methodology
ANOVA Parametric test: Biostatics and Research Methodology
 
3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptx3.12.24 The Social Construction of Gender.pptx
3.12.24 The Social Construction of Gender.pptx
 
3.14.24 The Selma March and the Voting Rights Act.pptx
3.14.24 The Selma March and the Voting Rights Act.pptx3.14.24 The Selma March and the Voting Rights Act.pptx
3.14.24 The Selma March and the Voting Rights Act.pptx
 
LEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced StudLEAD6001 - Introduction to Advanced Stud
LEAD6001 - Introduction to Advanced Stud
 
Research Methodology and Tips on Better Research
Research Methodology and Tips on Better ResearchResearch Methodology and Tips on Better Research
Research Methodology and Tips on Better Research
 
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - HK2 (...
 
The First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdfThe First National K12 TUG March 6 2024.pdf
The First National K12 TUG March 6 2024.pdf
 
3.12.24 Freedom Summer in Mississippi.pptx
3.12.24 Freedom Summer in Mississippi.pptx3.12.24 Freedom Summer in Mississippi.pptx
3.12.24 Freedom Summer in Mississippi.pptx
 
Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...
Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...
Certification Study Group - Professional ML Engineer Session 3 (Machine Learn...
 
Metabolism of lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptx
Metabolism of  lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptxMetabolism of  lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptx
Metabolism of lipoproteins & its disorders(Chylomicron & VLDL & LDL).pptx
 
Pharmacology chapter No 7 full notes.pdf
Pharmacology chapter No 7 full notes.pdfPharmacology chapter No 7 full notes.pdf
Pharmacology chapter No 7 full notes.pdf
 
Quantitative research methodology and survey design
Quantitative research methodology and survey designQuantitative research methodology and survey design
Quantitative research methodology and survey design
 
Plant Tissue culture., Plasticity, Totipotency, pptx
Plant Tissue culture., Plasticity, Totipotency, pptxPlant Tissue culture., Plasticity, Totipotency, pptx
Plant Tissue culture., Plasticity, Totipotency, pptx
 

Η Επιστήμη των Δικτύων: Μια Πολύ Σύντομη Εισαγωγική Παρουσίαση - 8 Οκτωβρίου 2014

  • 1. H Epist mh twn DiktÔwn Mia PolÔ SÔntomh Eisagwgik  ParousÐash Mwus c A. MpountourÐdhc Tm ma Majhmatik¸n PanepisthmÐou Patr¸n mboudour@upatras.gr Okt¸brioc 2014 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 2. Perieqìmena Basikèc 'Ennoiec DiktÔwn Mia Panoramik  'Ekjesh Diktuak¸n 'Ergwn LÐga Endeiktikˆ ParadeÐgmata Diktuak¸n Upologism¸n EndeiktikoÐ Pìroi Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 3. Basikèc 'Ennoiec DiktÔwn Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 4. Ti eÐnai èna dÐktuo; Praktikˆ, ètsi ìpwc katalabaÐnoume ennoiologikˆ ti eÐnai èna dÐktuo: 'Ena dÐktuo eÐnai èna sÔnolo paragìntwn   forèwn drˆshc, pou onomˆzontai dr¸ntec (actors), oi opoÐoi sqetÐzontai metaxÔ touc me kˆpoia morf¸mata diadrastik c sumperiforˆc, pou onomˆzontai desmoÐ (ties)   sqèseic diˆdrashc (interactions). Tupikˆ, ètsi ìpwc analÔetai majhmatikˆ (sthn JewrÐa Grˆfwn [Graph Theory]) kai anaparÐstatai mèsw grafik¸n optikopoi sewn (visualizations): 'Ena dÐktuo eÐnai èna sÔnolo kìmbwn (  koruf¸n   shmeÐwn), oi opoÐoi sundèontai metaxÔ touc me kˆpoia sugkekrimèna morf¸mata sundèsmwn (links). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 5. Kathgoriopoi seic Diktuak¸n Dr¸ntwn Oi dr¸ntec enìc diktÔou mporeÐ na eÐnai: 'Atoma (ˆnjrwpoi) me diaforetikˆ dhmografikˆ qarakthristikˆ (ìpwc fÔlo, ful –èjnoc, uphkoìthta, hlikÐa, ekpaÐdeush, ergasÐa, oikonomik  katˆstash, katoikÐa klp.)   se diaforetikèc yuqo–swmatikèc katastˆ- seic [pq., asjèneiec, ugeÐa, bˆroc, eutuqÐa klp.]   me diafo- retikèc idèec–pepoij seic–topojet seic–protim seic gia kˆpoia politistikˆ   politikˆ   oikonomikˆ klp. zht mata. Omˆdec atìmwn (ìpwc organ¸seic, etairÐec, jesmikˆ s¸mata, krˆth klp.). OrganismoÐ (zwikoÐ   biologikoÐ). Ulikˆ prˆgmata (ìpwc biblÐa, ergasÐec, episthmonikoÐ klˆdoi, mèsa epikoinwnÐac–plhrofìrhshc, teqnourg mata [artifacts], emporeÔmata, mhqanèc, upologistèc, diadiktuakˆ sˆðt/selÐdec klp.). Sunajroistikˆ gegonìta (ìpwc sumfwnÐec, yhfoforÐec, ekjèseic, diadhl¸seic diamarturÐac, sumbˆnta, peristˆseic, taktikèc sunant seic se q¸rouc epikoinwnÐac atìmwn   organ¸sewn gia sugkekrimènouc skopoÔc klp.). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 6. Kathgoriopoi seic Diktuak¸n Diadrˆsewn Oi diadrˆseic se èna dÐktuo mporeÐ na eÐnai: Koinwnikèc sqèseic metaxÔ atìmwn (ìpwc filÐac, suggèneiac, sunaisjhmatik c fÔshc, sexoualik c sqèshc, arèskeiac–dusarèskeiac, empistosÔnhc–duspistÐac klp.). Koinwnikèc sqèseic allhlexˆrthshc (ìpwc didˆsko- nta–didaskìmenou, proðstˆmenou–ufistˆmenou, sunergasÐac, upost rixhc, allhlobo jeiac, paroq c sumboul¸n, emporik¸n–oikonomik¸n sunallag¸n klp.). Koinwnikèc sqèseic antipalìthtac (ìpwc diafwnÐac, antiparajèsewn, èqjrac, fìbou, antagwnismoÔ klp.). 'Emmesec sqèseic diamoirasmoÔ   summetoq c se koinˆ gegonìta (ìpwc se organ¸seic, sumbˆnta, lèsqec–klamp, sullìgouc, sumboÔlia, sqoleÐa, jesmoÔc–idrÔmata, katagwg c   diamon c se gewgrafikèc perioqèc, sun–dhmosieÔsewn, bibliografik¸n anafor¸n, diˆdoshc gn¸shc, koinwnik c epirro c, koin¸n asqoli¸n, epanalambanìmenwn sunhjei¸n, ìpwc qr shc narkwtik¸n, klp., metˆdoshc [contagion] asjenei¸n k.ˆ.   diˆqushc i¸n k.ˆ. klp.). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 7. Qarakthristikˆ Dr¸ntwn kai Diadrˆsewn Diaforetikèc kathgorÐec (  tÔpoi) dr¸ntwn   diadrˆsewn mporoÔn na enopoihjoÔn se omˆdec, stic opoÐec orÐzetai èna qarakthristikì (attribute), pou paÐrnei diaforetikèc timèc se kˆje omˆda. Genik¸c, kˆje qarakthristikì mporeÐ na jewrhjeÐ wc mia metablht , eÐte posotik  (suneq¸n   diakrit¸n tim¸n)   poiotik  (diataktik¸n [ordinal]   onomastik¸n] [nominal] tim¸n). P.q.: 'Arrenec kai j leic dr¸ntec omadopoioÔntai kˆtw apì to (poiotikì) onomastikì qarakthristikì tou fÔlou. Dr¸ntec diaforetikoÔ bˆrouc omadopoioÔntai kˆtw apì to (posotikì) suneqèc qarakthristikì tou bˆrouc. Diadrˆseic hlektronik c epikoinwnÐac omadopoioÔntai kˆtw apì to (posotikì) diakritì qarakthristikì tou pl jouc   thc suqnìthtac twn antallassìmenwn mhnumˆtwn (se kˆpoia perÐodo). Diadrˆseic diaforetik¸n bajm¸n thc sqèshc filÐac omadopoioÔ- ntai kˆtw apì to (poiotikì) diataktikì qarakthristikì thc diabˆjmishc thc èntashc thc sqèshc filÐac. Diadrˆseic sumpˆjeiac–antipˆjeiac omadopoioÔntai kˆtw apì to (poiotikì) diataktikì (duadikì) qarakthristikì tou prìshmou (jetikoÔ   arnhtikoÔ) thc sqèshc. Oi antÐstoiqoi grˆfoi eÐnai oi grˆfoi me bˆrh   (timèc) (weighted– valued graphs) stouc kìmbouc   stouc sundèsmouc. Eidikˆ sto teleu- taÐo parˆdeigma, onomˆzontai proshmasmènoi grˆfoi (signed graphs). 'Ena dÐktuo, sto opoÐo oi Ðdioi dr¸ntec diathroÔn perissìterec thc miac diaforetikèc diadrˆseic onomˆzetai polusqidèc (multiplex). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 8. Diktuakèc AnalÔseic 1 Koinwnikˆ Diktuakˆ Dedomèna Erwthmatolìgia kai sunenteÔxeic Istorikˆ arqeÐa kai arqeÐa tÔpou Bibliometrikˆ kai episthmometrikˆ dedomèna Dedomèna apì to Internet (mhnÔmata, istoselÐdec, mplogk, koinwnikˆ mèsa) Sqesiakˆ Megˆla Dedomèna (Big Data) kai Anoiktˆ Dedomèna (Open Data) 2 Diktuakˆ Mètra BajmoÐ kìmbwn – Istogrˆmmata Kentrikìthtec kìmbwn Suntelest c suss¸reushc kai metabatikìthta Amoibaiìthta sundèsmwn Apostˆseic kìmbwn Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 9. 3 DiktuakoÐ diamerismoÐ Sunektikèc sunist¸sec kai klÐkec k–pur nec Pur nac–perifèreia IsodunamÐec kìmbwn (domik  kai kanonik ) OmadopoÐhsh se mplok Blockmodeling Koinìthtec (Communities) Taxinomhsimìthta (assortativity) kai anˆmeixh (mixing) 4 Qronik¸c Exart¸mena DÐktua Troqièc metabˆsewn 5 Statistik  JewrÐa DiktÔwn Exponential Random Graph Models (ERGM) 6 Montelopoi seic DiktÔwn Koinwnik  epirro  Diˆqush (montèla SIR kai SIS) TuqaÐoi grˆfoi Erd¨os–Re´ nyi DÐktua mikr¸n kìsmwn (small–worlds) DÐktua qwrÐc klÐmaka (scale–free) Auxanìmena tuqaÐa dÐktua kai to montèlo Bara´ basi–Albert Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 10. Mia Panoramik  'Ekjesh Diktuak¸n 'Ergwn Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 11. To DÐktuo twn Flwrentian¸n OÐkwn Sq ma: To dÐktuo twn gˆmwn metaxÔ twn megˆlwn OÐkwn thc FlwrentÐac tou mesaÐwna (Padgett & Ansell, Robust action and the rise of the Medici, 1400–1434, American Journal of Sociology, 1993, 98(6): 1259­1319). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 12. To DÐktuo twn Sten¸n Sunergat¸n tou Santˆm Sq ma: To dÐktuo tou eswterikoÔ kÔklou twn sten¸n sunergat¸n tou Santˆm Qouseòn (Baraba´ si et al., Network Science Book, http://barabasilab.neu.edu/networksciencebook/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 13. DÐktuo FilÐac Mel¸n Lèsqhc Karˆte Sq ma: DÐktuo filÐac twn 34 mel¸n miac Panepisthmiak c lèsqhc karˆte (Zachary, An information flow model for conflict and fission in small groups, Journal of Anthropological Research, 1977, 33: 452­473). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 14. DÐktuo Sunaisjhmatik¸n Sqèsewn Sq ma: DÐktuo sunaisjhmatik¸n–erwtik¸n sqèsewn (Bearman et al., Chains of affection: The structure of adolescent romantic and sexual networks, American Journal of Sociology, 2004, 110: 44­91) se optikopoÐhsh tou Mark Newman (http://www-personal.umich.edu/~mejn/networks/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 15. To dÐktuo twn AjlÐwn tou BÐktwroc Ougk¸ Sq ma: To dÐktuo twn sqèsewn metaxÔ twn kÔriwn qarakt rwn twn AjlÐwn tou BÐktwroc Ougk¸ (ta qr¸mata antistoiqoÔn se koinìthtec, pou upologÐsjhkan ek twn ustèrwn) (Newman & Girvan, Finding and evaluating community structure in networks, Physical Review E, 2004, 69: 026113). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 16. KuriarqoÔntec kìmboi kai koinìthtec sto dÐktuo twn AjlÐwn Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 17. DÐktuo PaqÔsarkwn Atìmwn Sq ma: DÐktuo paqÔsarkwn atìmwn (Christakis & Fowler, The spread of obesity in a large social network over 32 years, New Englnd Journal of Medicine, 2007, 357(4): 370­379) [Mègejoc kìmbwn BMI, kÐtrinoi paqÔsarkoi, prˆsino mh paqÔsarkoi, mwb sundèseic filÐa, portokalÐ suggeneÐc.] Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 18. DÐktuo Eutuqismènwn Atìmwn Sq ma: DÐktuo eutuqismènwn atìmwn (Fowler & Christakis, Dynamic spread of happiness in a large social network: Longitudinal analysis over 20 years in the Framingham Heart Study, British Medical Journal, 2008, 337(768): a2338). Kìmboi tetragwnikoÐ gunaÐkec, kuklikoÐ ˆndrec, mple ligìtero eutuqeÐc, kÐtrino perissìtero eutuqeÐc, kìkkinec sundèseic filÐa, maÔrec suggeneÐc.] Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 19. DÐktuo FilÐac Majht¸n tou Faux Magnolia High School Sq ma: To dÐktuo filÐac 1461 majht¸n tou Faux Magnolia High School qwrÐc apomonwmènouc kìmbouc (Goudreau et al., A statnet Tutorial, Journal of Statistical Software, 2008, 24(9): 1­27). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 20. DÐktuo FilÐac Majht¸n tou Faux Magnolia High School me to Qarakthristikì tou 'Etouc FoÐthshc twn Majht¸n Sq ma: To dÐktuo filÐac 1461 majht¸n tou Faux Magnolia High School me to qarakthristikì tou ètouc foÐthshc twn majht¸n kai qwrÐc apomonwmènouc kìmbouc (Goudreau et al., A statnet Tutorial, Journal of Statistical Software, 2008, 24(9): 1­27). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 21. DÐktuo FilÐac me to Qarakthristikì thc Ful c twn Majht¸n Sq ma: 'Ena dÐktuo filÐac majht¸n me to qarakthristikì thc ful c twn majht¸n (kÐtrino = leukoÐ, prˆsino = maÔroi, kìkkino = ˆllhc ful c) kai qwrÐc apomonwmènouc kìmbouc (Moody, Race, school integration, and friendship segregation in America, American Journal of Sociology, 2001, 107: 679­716) se optikopoÐhsh tou Mark Newman (http://www-personal.umich.edu/~mejn/networks/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 22. DÐktuo SunergasÐac sthn Santa Fe Sq ma: DÐktuo sunergasÐac episthmìnwn tou InstitoÔtou Santa Fe (Girvan & Newman, Community structure in social and biological networks, Proceedings of the National Academy of Sciences of the USA, 2002, 99: 8271­8276). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 23. DÐktuo Parapomp¸n sthn KoinwniologÐa Sq ma: DÐktuo bibliografik¸n parapomp¸n sthn KoinwniologÐa apì dedomèna tou Jim Moody (http://orgtheory.wordpress.com/2009/08/14/sociologys-citation-core/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 24. To DÐktuo twn Qwr¸n me Megˆlo Qrèoc Sq ma: To dÐktuo twn qwr¸n me megˆla qrèh (Baraba´ si et al., Network Science Book, http://barabasilab.neu.edu/networksciencebook/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 25. Trofikìc Istìc tou Oikosust matoc miac LÐmnhc Sq ma: To dÐktuo tou trofikoÔ istoÔ (food web) tou oikosust matoc thc LÐmnhc Little Rock tou Wisconsin (Martinez, Artifacts or attributes? Effects of resolution on the Little Rock Lake food web, Ecological Monographs, 1991, 61: 367­392). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 26. DÐktuo Fainotupik¸n Asjenei¸n Sq ma: DÐktuo fainotupik¸n asjenei¸n (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). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 27. To Internet Sq ma: To dÐktuo twn ISPs tou Internet (Cheswick & Burch, Internet Atlas Gallery, http://www.caida.org/projects/internetatlas/gallery/ches/data.xml). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 28. To Facebook Sq ma: To dÐktuo epikoinwnÐac tou Facebook (Baraba´ si et al., Network Science Book, http://barabasilab.neu.edu/networksciencebook/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 29. DÐktuo Twitter Sq ma: H gigantiaÐa sunektik  sunist¸sa enìc diktÔou Twitter gia kˆpoia RTs (retweets) pou èginan anaforikˆ me ta gegonìta diamarturÐac sthn TourkÐa ton IoÔnio tou 2013. Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 30. DÐktuo LinkedIn Sq ma: Oi koinoÐ – moirasmènoi (shared) – fÐloi gia duo qr stec tou LinkedIn. Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 31. DÐktuo (Dia–)Kleidwmènwn DS Etairi¸n (Interlocking Directorates) Sq ma: DÐktuo (Dia–)Kleidwmènwn (Interlocking Directorates) Dioikhtik¸n SumboulÐwn Etairi¸n apì koinèc summetoqèc steleq¸n se autèc (http://orgtheory.wordpress.com/2011/08/19/theyrule-net-interlocking-boards/, http://theyrule.net/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 32. To DÐktuo BioteqnologÐac–BiomhqanÐac stic HPA Sq ma: To dÐktuo twn sqèsewn BioteqnologÐac–BiomhqanÐac stic HPA (Powell, White, Koput & Owen–Smith, Network Dynamics and Field Evolution: The Growth of Interorganizational Collaboration in the Life Sciences, American Journal of Sociology, 2005, 110(4): 1132­1205, http://eclectic.ss.uci.edu/~drwhite/Movie/). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 33. DÐktuo Summetoq¸n se Koinwnikèc Ekdhl¸seic Gunaik¸n tou Nìtou Sq ma: DÐktuo summetoq¸n–maz¸xewn se 14 sumbˆnta koinwnik¸n ekdhl¸sewn 18 gunaik¸n tou Amerikˆnikou Nìtou (Davis, Gardner & Gardner, Deep Douth, University of Chicago Press, 1941). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 34. DÐktuo Yhfofori¸n sto An¸tero Dikast rio twn HPA Sq ma: DÐktuo yhfofori¸n sto An¸tero Dikast rio twn HPA me tic suneqìmenec grammèc na sumbolÐzoun jetikèc y fouc kai tic diakoptìmenec grammèc arnhtikèc y fouc (Mrvar & Doreian, Partitioning signed two­mode networks, Journal of Mathematical Sociology, 2009, 33: 196­221). Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 35. DÐktuo Epitrop¸n sthn Boul  twn Antipros¸pwn twn ARTICLE HPA IN PRESS BUDGET VETERANS’ AFFAIRS ARMED SERVICES AGRICULTURE 420 M.A. Porter et al. / Physica A 386 (2007) 414–438 APPROPRIATIONS INTELLIGENCE HOUSE ADMINISTRATION ENERGY/COMMERCE OFFICIAL CONDUCT HOMELAND SECURITY GOVERNMENT REFORM WAYS AND MEANS INTERNATIONAL RELATIONS TRANSPORTATION SMALL BUSINESS EDUCATION SCIENCE FINANCIAL SERVICES RULES RESOURCES JUDICIARY Sq ma: Fig. 4. (Color) Network of committees (squares) and subcommittees (circles) in the 108th US House of Representatives, color-coded by the DÐktuo parent standing epitrop¸n and select committees. (tetrˆgwna(The depicted ) labels kai indicate upo–the epitrop¸n parent committee (of kÔkloieach group ) sthn but do not 108identify h Boul  the twn Antipros¸pwn 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 Kamada–Kawai spring embedder, with link strengths (again indicated by darkness) determined by normalized interlocks. Observe structure again that subcommittees in the United of the States House of Representatives, same parent committee Physica are closely A, connected 2007, to each 386: other. 414­438). Oi sundèseic anaparistoÔn koinèc summetoqèc bouleut¸n se (upo)epitropèc. Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn Security Committee shares only one common member (normalized interlock 2.4) with the Intelligence Select Committee (located near the 1 o’clock position in Fig. 5) and has no interlock at all with any of the four
  • 36. LÐga Endeiktikˆ ParadeÐgmata Diktuak¸n Upologism¸n Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 37. BasikoÐ SumbolismoÐ JewrÐac Grˆfwn 'Enac grˆfoc G eÐnai èna zeÔgoc (V, E), ìpou to V eÐnai èna sÔnolo koruf¸n (  kìmbwn   shmeÐwn) kai to E eÐnai èna sÔnolo akm¸n (  gramm¸n   sundèsmwn   sundèsewn). 'Etsi, o grˆfoc grˆfetai wc G = (V, E) ki, ìtan qreiˆzetai na epishmˆnoume ìti to V eÐnai to sÔnolo koruf¸n tou grˆfou G, grˆfoume V = V(G) kai, parìmoia, ìti to E eÐnai to sÔnolo akm¸n tou G, grˆfoume E = E(G). Kˆje akm  e 2 E enìc grˆfou G = (V, E) antistoiqeÐ se duo korufèc tou sunìlou V, oi opoÐec apoteloÔn ta duo ˆkra thc akm c. 'Otan ta ˆkra thc akm c e 2 E eÐnai oi korufèc u kai v 2 V, grˆfoume e = (u, v). Shmeiwtèon ìti oi akmèc den èqoun kateÔjunsh, dhlad , e = (u, v) = (v, u). O grˆfoc 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 2 v1 v2 ❅ ❅ v4 v3 ❅ ❅ V = {v1, Mwus c v2, Av3}, . MpountourÐdhc E = {{v3, H Epist mh v4}, {v2, twn v3}, DiktÔwn {v1, v3}}
  • 38. observe that G1 ⊕ G2 = G1 ∪ G2. However, usually for ring sums we have the same vertex TÔpoi Grˆfwn = 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 brìqoc (loop) eÐnai mia akm  pou en¸nei mia koruf  v me ton eautì thc, e = (v, v). Duo (  perissìterec) akmèc onomˆzontai parˆllhlec an ta ˆkra touc eÐnai oi Ðdiec korufèc. 'Enac grˆfoc qwrÐc brìqouc kai qwrÐc parˆllhlec akmèc onomˆzetai aplìc, en¸ diaforetikˆ onomˆzetai pollaplìc grˆfoc (multi–graph). 'Enac grˆfoc onomˆzetai grˆfoc me bˆrh (weighted graph) kai sumbolÐzetai wc G = (V, E,w), an se kˆje akm  tou e antistoiqeÐ èna bˆroc   mia tim  w(e) 2 R. Directed Graphs Definition 10 directed 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 kateujunìmenoc grˆfoc   digrˆfoc G eÐnai èna zeÔgoc (V, E), ìpou to V eÐnai èna sÔnolo koruf¸n (  kìmbwn   shmeÐwn) kai to E eÐnai èna sÔnolo tìxwn me to kˆje tìxo e 2 E na antistoiqeÐ se èna diatetagmèno zeÔgoc koruf¸n (u, v) ètsi ¸ste na kateujÔnetai apì thn koruf  u proc thn koruf  v. O kateujunìmenoc grˆfoc 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 associated with the edge e they are called the endpoints of e, we often write uv or (u, v) to represent the arc e. Example 11 v1 ❅ ✻ ❅ v4 v2 v3 ❅ ❅❘ ✲ V Mwus c = {v1, A. v2, MpountourÐdhc v3}, E = {(v4, H v3), Epist mh (v3, twn v2), DiktÔwn (v1, v3)}
  • 39. DimereÐc Grˆfoi 'Enac grˆfoc onomˆzetai dimer c (bipartite), ìtan upˆrqei ènac diamerismìc tou sunìlou twn koruf¸n tou V se duo mèrh (tm mata), to U kai to W, dhlad , V = U [W (ìpou U W = ?), ètsi ¸ste ìlec oi akmèc na phgaÐnoun apì to U sto W kai na mhn upˆrqei kamiˆ akm  oÔte metaxÔ koruf¸n tou U oÔte metaxÔ koruf¸n tou W. Probolèc dimeroÔc grˆfou: u1 u3 u2 u4 u1 u2 u3 u4 w1 w2 w3 w2 w1 w3 1 2 2 1 1 2 1 2 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 40. BajmoÐ Kìmbwn GeÐtonec: 'Estw o mh kateujunìmenoc grˆfoc G = (V, E) kai i, j 2 V duo korufèc tou. H j lègetai geÐtonac thc i ìtan (i, j) 2 E. PÐnakac GeitnÐashc (Adjacency Matrix): EÐnai ènac (summetrikìc) pÐnakac A = fAgi,j2V tˆxhc jVj jVj tètoioc ¸ste A = 1, ìtan i, j geÐtonec, A = 0, diaforetikˆ. BajmoÐ: Sto mh kateujunìmeno grˆfo G, o bajmìc miac koruf c i, pou sumbolÐzetai wc ki, orÐzetai san to pl joc twn geitìnwn tou i, dhlad , to pl joc twn sundèsewn pou prospÐptoun sto i. Profan¸c, isqÔei: ki = X j2V A = X i2V A ki, epiplèon, X i2V ki = X i,j2V A = 2jEj Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 41. 'Estw t¸ra o kateujunìmenoc grˆfoc G = (V, E), gia ton opoÐon o antÐstoiqoc pÐnakac geitnÐashc A = fAg eÐnai mh summetrikìc. O bajmìc eisìdou thc koruf c i tou G, pou sumbolÐzetai wc kin i , orÐzetai san to pl joc twn sundèsewn pou xekinoÔn apì geÐtonec tou i kai kateujÔnontai proc ton i, dhlad , kin i = X j2V A O bajmìc exìdou thc koruf c i tou G, pou sumbolÐzetai wc kout i , orÐzetai san to pl joc twn sundèsewn pou xekinoÔn apì ton i kai kateujÔnontai proc geÐtonec tou i, dhlad , kout i = X i2V A Profan¸c, isqÔei: X i2V kin i = X j2V kout i = X i,j2V A = jEj Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 42. BajmoÐ kìmbwn sto dÐktuo karˆte Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 43. GenikoÐ TÔpoi Diktuak¸n Katanom¸n Bajm¸n Sq ma: Diwnumik  Katanom  (  Katano- m  Poisson) gia tuqaÐouc grˆfouc Erd¨os–Re´ nyi Sq ma: Katanom  Nìmou DÔnamhc (Power Law) gia dÐktua qwrÐc klÐmaka (scale–free networks) Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 44. Kentrikìthtec Kìmbwn: 1. Kentrikìthta BajmoÔ (Degree Centrality) Oi orismoÐ OLWN twn kentrikìthtwn pou ja d¸soume ed¸ kai sth sunèqeia aforoÔn mh kateujunìmenouc (aploÔc) grˆfouc. H kentrikìthta bajmoÔ (degree centrality) xi tou kìmbou i isoÔtai proc ton bajmì ki tou kìmbou autoÔ: xi = ki x8 = 5 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 45. 2. Kentrikìthta Endiamesìthtac (Betweenness Centrality) H kentrikìthta endiamesìthtac (betweenness centrality) xi tou kìmbou i isoÔtai proc: xi = X s6=i6=t2V nist gst ìpou nist eÐnai to pl joc twn gewdaitik¸n diadrom¸n metaxÔ twn kìmbwn s kai t, pou pernoÔn apì ton kìmbo i, kai gst eÐnai to sunolikì pl joc twn gewdaitik¸n diadrom¸n metaxÔ twn kìmbwn s kai t. n23 ,23 = 2 g3,23 = 4 x2 = 0.1436 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 46. 3. Kentrikìthta EggÔthtac (Closeness Centrality) Se ènan grˆfo G, gia kˆje duo kìmbouc i, j, h (gewdaitik ) apìstas  touc d(i, j) orÐzetai wc to m koc thc suntomìterhc diadrom c apì to i sto j, efìson oi kìmboi autoÐ eÐnai sundedemènoi, en¸ d(i, j) = 1, diaforetikˆ (kai fusikˆ, d(i, i) = 0). (H ‘‘suntomìterh diadrom ’’ metaxÔ duo kìmbwn eÐnai h diadrom  pou èqei to elˆqisto m koc anˆmesa se ìlec tic diadromèc metaxÔ twn duo kìmbwn.) Se ènan grˆfo me n kìmbouc, h kentrikìthta eggÔthtac (closeness centrality) xi tou kìmbou i isoÔtai proc: xi = n P j2V d(i, j) x0 = 0.5689 x2 = 0.5593 x33 = 0.55 x31 = 0.5409 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 47. 4. Kentrikìthta IdiodianÔsmatoc (Eigenvector Centrality) H kentrikìthta idiodianÔsmatoc (eigenvector centrality) xi tou kìmbou i isoÔtai proc: xi = 1 1 X j2V Axj ìpou A eÐnai o pÐnakac geitnÐashc (adjacency matrix) tou grˆfou kai xi eÐnai oi sunist¸sec tou idiadianÔsmatoc tou A, pou antistoiqoÔn sth megalÔterh idiotim  tou 1. x33 = 0.3734 x0 = 0.3555 x2 = 0.3172 x32 = 0.3086 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 48. Oi 4 kentrikìthtec twn kìmbwn tou diktÔou karˆte Nodes Degree C. Betweenness C. Closeness C. Eigenvector C. 0 0.484848485 0.437635281 0.568965517 0.355490721 1 0.272727273 0.053936688 0.485294118 0.265959605 2 0.303030303 0.143656806 0.559322034 0.317192417 3 0.181818182 0.011909271 0.464788732 0.211179694 4 0.090909091 0.000631313 0.379310345 0.075968879 5 0.121212121 0.029987374 0.38372093 0.079483113 6 0.121212121 0.029987374 0.38372093 0.079483113 7 0.121212121 0 0.44 0.170959892 8 0.151515152 0.055926828 0.515625 0.227404355 9 0.060606061 0.000847763 0.434210526 0.102674504 10 0.090909091 0.000631313 0.379310345 0.075968879 11 0.03030303 0 0.366666667 0.052855817 12 0.060606061 0 0.370786517 0.084254727 13 0.151515152 0.045863396 0.515625 0.226473112 14 0.060606061 0 0.370786517 0.10140365 15 0.060606061 0 0.370786517 0.10140365 16 0.060606061 0 0.284482759 0.023635566 17 0.060606061 0 0.375 0.092399699 18 0.060606061 0 0.370786517 0.10140365 19 0.090909091 0.032475048 0.5 0.147912918 20 0.060606061 0 0.370786517 0.10140365 21 0.060606061 0 0.375 0.092399699 22 0.060606061 0 0.370786517 0.10140365 23 0.151515152 0.017613636 0.392857143 0.150118912 24 0.090909091 0.002209596 0.375 0.057052326 25 0.090909091 0.003840488 0.375 0.059206342 26 0.060606061 0 0.362637363 0.075579616 27 0.121212121 0.022333454 0.458333333 0.133477386 28 0.090909091 0.001794733 0.452054795 0.131077964 29 0.121212121 0.002922078 0.38372093 0.134961122 30 0.121212121 0.014411977 0.458333333 0.174758637 31 0.181818182 0.138275613 0.540983607 0.191034394 32 0.363636364 0.145247114 0.515625 0.308643749 33 0.515151515 0.304074976 0.55 0.373362539 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 49. Kentrikìthta Mikr  tim  Megˆlh tim  Degree LÐgoi geÐtonec (sundèseic) PolloÐ geÐtonec (sundèseic) Betweenness Mikrìc èlegqoc ro c Megˆloc èlegqoc ro c Closeness Proc thn perifèreia Proc to kèntro Eigenvector LÐgoi   lÐgo shmantikoÐ geÐtonec PolloÐ   polÔ shmantikoÐ geÐtonec To dÐktuo twn stratiwtik¸n tou David Krackhardt: Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 50. Suntelest c Suss¸reushc O suntelest c suss¸reushc (clustering coefficient) Ci tou kìmbou i orÐzetai wc: Ci = 2i ki(ki 1) ìpou i eÐnai to pl joc twn sundèsewn metaxÔ twn geitonik¸n kìmbwn tou i kai d i proc opoiod pote ˆllo kìmbo ki eÐnai to pl joc twn geitonik¸n kìmbwn tou i. C23 = 2 4 5 4 = 0.4 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 51. Diktuak  Metabatikìthta O sunolikìc suntelest c suss¸reushc (global clustering coefficient) (ìlou) tou grˆfou G orÐzetai wc h mèsh tim  twn suntelest¸n suss¸reushc twn kìmbwn tou: C(G) = 1 jVj X i Ci H metabatikìthta (transitivity) tou grˆfou G orÐzetai wc to phlÐko: T(G) = pl joc trig¸nwn pl joc sundedemènwn triˆdwn C(G) = 0.16 T(G) = 0.19 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 52. Amoibaiìthta Sundèsewn se Kateujunìmeno Grˆfo Se ènan kateujunìmeno grˆfo, o suntelest c amoibaiìthtac sundèsewn/desm¸n (link/tie mutuality coefficient) orÐzetai wc ex c: M(G) = pl joc antapodidìmenwn sundèsewn Er pl joc ìlwn twn sundèsewn/tìxwn E Er(G) = 64 E(G) = 195 M(G) = 0.3282 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 53. Apostˆseic Kìmbwn se Grˆfo SumbolÐzontac me d(i, j) th (gewdaitik ) apìstash ston grˆfo G metaxÔ twn duo kìmbwn i, j (dhlad , wc m koc thc suntomìterhc diadrom c apì to i sto j, efìson oi kìmboi autoÐ eÐnai sundedemènoi, en¸ d(i, j) = 1, ìpou h ‘‘suntomìterh diadrom ’’ metaxÔ duo kìmbwn eÐnai h diadrom  pou èqei to elˆqisto m koc anˆmesa se ìlec tic diadromèc metaxÔ twn duo kìmbwn), to mèso m koc twn suntomìterwn diadrom¸n (average shortest path length) ston grˆfo autì, orÐzetai wc: a = 1 jVj(jVj 1) X i,j2V d(i, j) a = 2.4082 Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 54. Mètra Diˆforwn Empeirik¸n DiktÔwn TABLE I. The general characteristics of several real networks. For each network we indicated the number of nodes, the average degree !k, the average path length ! and the clustering coefficient C. For a comparison we have included the average path length !rand and clustering coefficient Crand of a random graph with the same size and average degree. The last column identifies the symbols in Figs. 8 and 9. Network Size !k ! !rand C Crand Reference Nr. WWW, site level, undir. 153, 127 35.21 3.1 3.35 0.1078 0.00023 Adamic 1999 Internet, domain level 3015 - 6209 3.52 - 4.11 3.7 - 3.76 6.36 - 6.18 0.18 - 0.3 0.001 Yook et al. 2001a, Pastor-Satorras et al. 2001 Movie actors 225, 226 61 3.65 2.99 0.79 0.00027 Watts, Strogatz 1998 LANL coauthorship 52, 909 9.7 5.9 4.79 0.43 1.8 × 10−4 Newman 2001a,b MEDLINE coauthorship 1, 520, 251 18.1 4.6 4.91 0.066 1.1 × 10−5 Newman 2001a,b SPIRES coauthorship 56, 627 173 4.0 2.12 0.726 0.003 Newman 2001a,b,c NCSTRL coauthorship 11, 994 3.59 9.7 7.34 0.496 3 × 10−4 Newman 2001a,b Math coauthorship 70, 975 3.9 9.5 8.2 0.59 5.4 × 10−5 Barab´asi et al. 2001 Neurosci. coauthorship 209, 293 11.5 6 5.01 0.76 5.5 × 10−5 Barab´asi et al. 2001 E. coli, substrate graph 282 7.35 2.9 3.04 0.32 0.026 Wagner, Fell 2000 10 E. coli, reaction graph 315 28.3 2.62 1.98 0.59 0.09 Wagner, Fell 2000 11 Ythan estuary food web 134 8.7 2.43 2.26 0.22 0.06 Montoya, Sol´e 2000 12 Silwood park food web 154 4.75 3.40 3.23 0.15 0.03 Montoya, Sol´e 2000 13 Words, cooccurence 460.902 70.13 2.67 3.03 0.437 0.0001 Cancho, Sol´e 2001 14 Words, synonyms 22, 311 13.48 4.5 3.84 0.7 0.0006 Yook et al. 2001 15 Power grid 4, 941 2.67 18.7 12.4 0.08 0.005 Watts, Strogatz 1998 16 C. Elegans 282 14 2.65 2.25 0.28 0.05 Watts, Strogatz 1998 17 TABLE II. The scaling exponents characterizing the degree distribution of several scale-free networks, for which P(k) follows a power-law (2). We indicate the size of the network, its average degree !k and the cutoff for the power-law scaling. For directed networks we list separately the indegree (#in) and outdegree (#out) exponents, while for the undirected networks, marked with a star, these values are identical. The columns lreal , lrand and lpow compare the average path length of real networks with power-law degree distribution and the prediction of random graph theory (17) and that of Newman, Strogatz and Watts (2000) (62), as discussed in Sect. V. The last column identifies the symbols in Figs. 8 and 9. Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 55. EndeiktikoÐ Pìroi Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 56. Pìroi gia Eisagwg  sta Koinwnikˆ DÐktua 1 BiblÐa Mark Newman, Networks: An Introduction, Oxford University Press, 2010. Stanley Wasserman and Katherine Faust, Social Network Analysis: Methods and Applications, Cambridge University Press, 1994. 2 'Arjra Episkìphshc Mark Newman, The structure and function of complex networks: http://arxiv.org/pdf/cond-mat/0303516v1 Laszlo Bara´ basi et al., Network Science Book: http://barabasilab.neu.edu/networksciencebook/ Robert A. Hanneman and Mark Riddle, Introduction to social network methods: http://faculty.ucr.edu/~hanneman/nettext/ Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn
  • 57. 3 Logismikì NetworkX: http://networkx.github.io/ Gephi: http://gephi.github.io/ Pajek: http://pajek.imfm.si/doku.php UCInet: https://sites.google.com/site/ucinetsoftware/home iGraph: http://igraph.sourceforge.net/ Mwus c A. MpountourÐdhc H Epist mh twn DiktÔwn