redes oscuras.docx

7/25/2019 redes oscuras.docx

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o'10or ?.c^oy t.]*>

Tracking, Destabilizing and Disr!ting Dark "et#orks #it$ %ocial"et#orks &nalysis%ean . ()erton "a)al ostgradate %c$ool

+ersion 1.0T&-(//"T("T%$a!ter 1.................................2ntrodction 1$a!ter 3 %ocial "et#ork &nalysis Ter4s, once!ts and&ss4!tions 10$a!ter 56etting %tarted #it$ 72"(T, "etDra# and a8ek 50$a!ter 9 6at$ering, ollecting, :ani!lating and+isalizing %ocial"et#ork Data T$e -asics.............................3$a!ter ..........................."et#ork To!ogra!$y ;3$a!ter


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-eCore atte4!ting to se social net#ork analysis, researc$ersneed to Cirst de)elo! a #orking i.e., tentati)eE $y!ot$esis asto $o# best to disr!t t$e dark net#ork t$ey are analyzing. %o4e,Cor e@a4!le, 4ay decide t$at t$e best a!!roac$ is to Cocs on t$enet#orkAs Cinancial ties, belie)ing t$at by s$tting do#n or

disr!ting t$e Clo# oC Cnds, it #ill be diCCiclt Cor t$enet#ork to Cinance o!erations. /t$ers 4ay conclde t$at targetinga net#orkAs o!erational ties oCCers t$e best o!!ortnity Cordisr!tion, ass4ing t$at #it$ot its key o!erati)es, a net#ork#ill not $a)e t$e !ersonnel necessary to carry ot o!erations.%till ot$ers 4ay target a net#orkAs Criends$i!, kins$i!, sc$oolandKor religios ties since insrgencies tend to recrit ne#4e4bers t$rog$ close !ersonal ties oCland and %tark 1;


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1;;5E and sed by -reiger and attison 1;


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#$y social net#ork analysts oCten trn to ot$er 4et$ods #$en#orking #it$ large net#orks. or or !r!oses $ere, $o#e)er, #eCocs on recording data in 4atri@ Cor4.&ggregating "et#orks

&ctors are ty!ically in)ol)ed in 4ore t$an one ty!e oC

relation anne4an and Biddle 300E. or e@a4!le, 4ostindi)idals are e4bedded in a n4ber oC diCCerent ty!es oC ties,sc$ as Criends$i!, kins$i! and econo4ic. -siness organizationsare no diCCerent. T$ey engage in Cinancial and inCor4ationale@c$anges and so4eti4es Cor4 alliances #it$ one anot$er %a@enian1;;9E. T$e sa4e is tre #it$ contries. T$ey are e@!licitlylinked t$rog$ n4eros cltral, econo4ic, 4ilitary and!olitical ties, and i4!licitly linked t$rog$ ties created bytransnational cor!orations, nongo)ern4ental organizations andinternational agencies :eyer et al. 1;;=E. %c$ 4lti!le@ity isi4!ortant becase ties oCten !ll actors in diCCerent directions%i44el S1;0, 1;33] 1;E. or e@a4!le, or #ork ties 4ay !s$s in t$e direction oC 4aking one c$oice, #$ile or Criends$i!and kins$i! ties 4ay !ll s in anot$er. T$is sggests t$at iC #e#ant a 4ore3-ecase 4arriage ties are reci!rocal, a H1I not only a!!ears int$e &cciaiolN:edicci cell, bt also in t$e :edicciN&cciaiolcell.5+ersion 1.0accrate !ictre oC a net#orkAs dyna4ics, t$e 4ore ty!es oC ties#e record and aggregate toget$erE t$e better. H2ndeed it is abasic ass4!tion oC t$ose sbscribing to t$e net#ork a!!roac$

t$at be$a)ior cannot be e@!lained in ter4s oC any one singleacti)ityI -reiger 1;=, cited in &zarian, 3005;E.

T$is, oC corse, raises Gestions oC strategy and t$e codingoC social net#ork data. 2C #e #ant to disr!t a dark net#orkAsCinancial o!erations, #e 4ay #ant to only aggregate its Cinancialties e.g., ties oC Cinancial Clo#s bet#een actorsE and actorAsaCCiliations #it$ instittions t$at !ro)ide Cinancial s!!ort tot$e dark net#ork e.g., bsinesses, cri4inal acti)ities, andKorc$arities and Condations acting as a Cinancial Cront to t$enet#orkE. -t, #$at iC a net#orkAs Cinancial o!erations rely$ea)ily on ties oC trst bet#een actors? T$en #e 4ay #ant to

aggregate Criends$i! and kins$i! ties along #it$ a net#orkAsCinancial ties. /r, #e 4ay #ant to Cirst analyze only t$enet#orkAs Cinancial ties and t$en add t$e Criends$i! and kins$i!ties Cor additional analysis. learly, t$ere are no clearNctans#ers as to $o# and #$ic$ net#orks to aggregate. %c$ decisions$a)e to be 4ade on a caseNbyNcase basis.&nalysis :etrics and +isalization


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%ocial net#ork 4etrics !lay an i4!ortant role in analyzing asocial net#orkAs dyna4ics. Density and ot$er related 4easres can$el! researc$ers gain an o)erall nderstanding t$e o)erallHs$a!eI oC t$e net#ork i.e., its to!ogra!$yEL centrality4easres can $el! identiCy key and !eri!$eral actors #it$in a

net#orkL clstering algorit$4s can $el! locate )arios sbgro!s#it$in t$e larger net#ork and also !ro)ide additionalinCor4ation on t$e net#ork as a #$oleEL and brokerage 4easrescan $el! identiCy actors and ties bet#een actors t$at ser)e asc$annels Cor t$e e@c$ange and Clo# oC inCor4ation and ot$erresorces e.g., Cinancial, aCCectionE. %ocial net#ork analystsgenerally se a )ariety oC 4etrics rat$er t$an 8st one or t#oEin t$eir atte4!ts to gain an o)erall nderstanding oC a net#ork.

:etrics are not t$e only tool a)ailable to social net#orkanalysts, $o#e)er. "et#ork )isalization is anot$er $el!Cl toolt$at it can $el! s see !atterns t$at 4ay not be readily a!!arentby si4!ly looking at 4etrics astilla et al. 3000E. 2ndeed,so4eti4es #$en clstering algorit$4s are nsccessCl inidentiCying co$esi)e sbgro!s #it$in a net#ork, net#ork)isalization algorit$4s are. T$at is #$y bot$ 4etrics and)isalization are co4!li4entary !arts oC t$e social net#orkanalysis toolbo@. :ost social net#ork analysis !rogra4s eit$erco4e #it$ net#ork 4a!!ing algorit$4s e.g., a8ekE or integrate#it$ net#ork )isalization !rogra4s t$at do e.g., 72"(T and"etDra#E.9+ersion 1.02nter!retation

/nce #e Cinis$ analyzing a net#ork, #e need to inter!ret #$at#e $a)e Cond. Fe #ill #ant to ask Gestions sc$ asJ Does t$e net#ork as a #$ole e@$ibit any c$aracteristics e.g.,

density, centralization, clsteringE t$at 4ig$t sggest#$et$er it is 4ore or less eCCecti)e t$an ot$er co4!arablenet#orks?

J &re t$erekey actors or ties bet#een actors #$ose re4o)al Cro4t$e net#ork

#ill render it ineCCecti)e?J /r, are t$ere !eri!$eral actors t$at cold !ossibly be enticed

to lea)e t$e net#ork, t$s 4aking it 4ore )lnerable to

disr!tion, inCiltration or isolation?J &re t$eredistinct sbgro!s #it$in t$e larger net#ork t$atcold !ossibly betrned against one anot$er sc$ t$at t$e net#ork e@erts 4oreenergy on internal Cig$ts t$an e@ternal o!erations?J &re t$ereorganizations #it$in t$e net#ork e.g., sc$ools,bsinesses, Cait$


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co44nitiesE t$at are attracti)e targets Cor inCiltration toi4!ro)e or intelligence gat$ering ca!abilities?"eedless to say, t$e ans#ers #e gi)e to t$ese Gestions andot$ers inCor4 t$e strategies #e de)elo! and t$e !olicies #ereco44end.

De)elo!ing %trategies and olicy Beco44endations2t is i4!ortant to e4!$asize t$at t$e strategies #e de)elo!and t$e !olicies #e reco44end do not necessarily $a)e to in)ol)edirect action e.g., targeting key actors #it$in t$e net#ork Corre4o)al or ca!treE. T$ey cold instead in)ol)e indirect action2/ and syo!sE ca4!aigns t$at 4ani!late actors andKorrelations$i!s #it$in t$e net#ork, rendering it less eCCecti)e, ora4nesty ca4!aigns t$at atte4!t to reintegrate so4e net#ork4e4bers e.g., indi)idals or Cait$ co44nitiesE back into t$elarger co44nity, t$s #eakening t$e net#ork Cro4 t$e otside./r, t$ey cold in)ol)e targeting key instittions #it$in t$enet#ork Cor inCiltration, t$s i4!ro)ing or intelligencegat$ering and !ro)iding better net#ork dataE. T$e !oint $ere ist$at social net#ork analysis !ro)ides )arios #ays oC looking ata dark net#ork, #$ic$ in trn !ro)ides s #it$ !otentiallydiCCerent strategies Cor disr!ting t$e4.+ersion 1.0%44ary

2t is not an o)erstate4ent to state t$at t$e botto4 line oCt$is a!!roac$ to sing social net#ork analysis to track anddisr!t dark net#orks is to de)elo! strategies and 4ake related!olicy reco44endations. T$at is #$y t$is gide is 4c$ 4ore t$an

a 4et$odological $andbook. 2t is also $el!Cl to kee! in 4indt$at social net#ork analysis is only one tool a)ailable toresearc$ers. 2t is not a 4agic bllet t$at #ill singleN$andily#in t$e global #ar on terror. 2t is, $o#e)er a )alable tool t$at#$en sed in con8nction #it$ ot$er tools e.g., geos!atialanalysis, te4!oral analysis, cltral analysisE can !ro)e to beGite )alable.1.3 Dark "et#orks as roble4s

:any arge t$at becase oC t$eir ada!tability, net#orkstrctres as o!!osed to $ierarc$ical onesE are better sited tosol)ing nonrotine, co4!le@ andKor ra!idlyNc$anging H!roble4sI or

c$allenges 6rano)etter 1;L Baab and :il#ard 3005E. orinstance, &nnaee %a@enian 1;;9L 1;;


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t$at #as 4ore res!onsi)e to t$e )olatile $ig$ tec$nology indstryt$an #ere ot$er regional areas.

/C corse, Cor so4e t$e !roble4 to be Hsol)ed,I $o#e)er, isnot al#ays $o# to best de)elo! a regional $ig$Ntec$ econo4y btrat$er $o# to saCely engage in co)ert and illegal acti)ities sc$

as ar4s traCCicking, drg dealing, terroris4 or 4oney landeringBaab and :il#ard 3005E. 2t a!!ears t$at net#ork strctres are#ell sited Cor tackling t$ese ty!es oC !roble4s as #ell Vlerks3001L Vrebs 3001L Baab and :il#ard 3005E.

T$is creates certain !roble4s Cor t$ose #$o seek to disr!tt$e4. /ne is t$at becase oC t$eir net#ork strctre, co)ert andillegal i.e., darkE net#orks are Gick to ada!t to c$angingen)iron4ental !ressres. or instance, !rior to t$e %e!te4ber11t$attacks &l aeda #as so4e#$at )ertically integrated, atleast at t$e co44and and control le)elL since t$e 7.%. in)asionoC &Cg$anistan, $o#e)er, it a!!ears to $a)e beco4e Car 4oredecentralized Baab and :il#ard 300593E. T$is sggests t$atnet#ork data at Hti4e oneI 4ay be ot oC date at Hti4e t#o,I so#e continosly need to !date or data. &not$er !roble4 is t$atdark net#orks do not necessarily o!erate inde!endently Cro4 oneanot$er bt instead are oCten connected t$rog$ actors #$oCnction as brokers bet#een t$ese net#orks Baab and :il#ard300593E$ange DeCalt olderile>Te@t (ditorData>%!reads$eetsData>Dis!lay


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igre 5.1 72"(T 2nterCaceT$e ile 4en contains se)eral seCl Cnctions, t#o oC #$ic$

#e #ill discss $ere. /ne is t$e ile>$ange DeCalt olderco44and, #$ic$ tells 72"(T #$ere to look Cor social net#orkdata.11 F$en yo se 72"(T t$e Cirst ti4e, t$e deCalt Colder

s$old be H\rogra4 iles\&nalytic Tec$nologies\7cinetTe@t(ditor co44andL it o!ens :icrosoCtAs H"ote!adI !rogra4,#$ic$ can be sed Cor editing data Ciles its co4!anion s!eedbtton #as discssed in t$e !re)ios !aragra!$E.

T$e Data 4en incldes se)eral $el!Cl Cnctions as #ell. T$eData>%!reads$eets co44and accesses 72"(TAs internal s!reads$eet!rogra4 t$at analysts can se Cor creating and editing socialnet#ork 4atrices see discssion oC its co4!anion s!eed bttonabo)eE. T$e Data>Dis!lay co44and and its co4!anion s!eed bttonN see discssion abo)eE dis!lays 72"(T social72"(T $as a s!eed btton Cor t$is co44and in t$e lo#er rig$t$and corner oC its interCace.53+ersion 1.0

net#ork Ciles. To get a sense oC $o# t$is #orks, isse t$isco44and, #$ic$ #ill o!en a dialog bo@ si4ilar to t$at in igre5.3 belo#. %elect t$e VrackNig$N Tec.[[$ Cile and click H/!enI"ote &lt$og$ yo cannot see t$e VrackNig$N Tec.[[d Cile, itis in t$e Colder N iC it #as not, yo #old not be able todis!lay t$e data CileE.


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igre 5.3 72"(T Dis!lay Dialog -o@T$is brings ! a 72"(T ot!t log see igre 5.5 ne@t !ageE,

#$ic$ is generally $o# 72"(T dis!lays reslts andKorinCor4ation. "ote t$at t$e !!er leCt oC t$e ot!t log statesH:atri@ [1 &D+2(I. 2C yo scroll do#n t$e ot!t log, yo #illdisco)er t$at t$e Cile contains t#o 4ore net#orks B2("D%2 andB(/BT%RT/. Fe #ill !ost!one discssing $o# yo can and #$y yo4ig$t #ant toE HstackI net#orks in sc$ a #ay. or no# all yoneed to kno# t$at Da)id Vrack$ardt collected data on 31 4anagersoC a %ilicon +alley co4!any t$at 4anCactred $ig$Ntec$

eGi!4ent. (ac$ 4anager #as asked to #$o4 t$ey #ent Cor ad)iceand #$o t$ey considered t$eir Criends. Vrack$ardt also deter4inedto #$o4 eac$ 4anager re!orted Cro4 co4!any doc4ents.

& Z1A recorded in t$e cell oC t$e H&d)iceI net#ork indicatest$at t$e 4anager listed on t$e Car leCt seeks ad)ice Cro4 t$e4anager listed across t$e to!. or instance, yo can see inigre 5.5 t$at 4anager [1 seeks ad)ice Cro4 4anager [3, bt4anager [3 does not seek ad)ice Cro4 4anager [1. %i4ilarly, a Z1Arecorded in t$e cell oC t$e Hriends$i!I net#ork indicates t$att$e 4anager listed on t$e leCt considers t$e 4anager listedacross t$e to! to be a Criend, and a

55+ersion 1.0Z 1A recorded in t$e cell oC t$e HBe!orts toI net#ork indicatest$at t$e 4anager listed on t$e leCt re!orts to t$e 4anager listedacross t$e to!. Vrack$ardt also collected attribte data on t$e4anagers age in yearsE, lengt$ oC ser)ice or tenre in yearsE,le)el in t$e cor!orate $ierarc$y 1(/, 3 +ice resident, 5


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4anagerE and de!art4ent coded 1,3,5,9 #it$ t$e (/ in de!art4ent0E. T$ese data, $o#e)er, are stored in a diCCerent Cile./7T7T./63

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+igre 5.5 72"(T /t!t og

or no# #e #ill not e@!lore any oC t$e co44ands Cond ndert$e TransCor4, Tools or "et#ork 4ens. & Gick glance at t$eTransCor4 and Tools 4ens indicates t$at 72"(T incldes a n4ber

oC rotines Cor transCor4ing and analyzing social net#ork data.Fe #ill not tilize all oC t$ese co44ands in t$is gide, bt #e#ill se a Ce#. T$e co44ands t$at #ill occ!y 4ost oC or ti4eare Cond nder t$e "et#ork 4en. ere yo #ill Cind rotines Coresti4ating 4easres oC net#ork to!ogra!$y e.g., "et#ork>o$esion>Density, "et#ork>o$esion>lstering oeCCicient,"et#ork>o$esion>DensityE, calclating actor centrality e.g.,"et#ork>entrality>Degree, "et#ork> entrality>ree4an


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-et#eenness, "et#ork>entrality>loseness, "et#ork>entrality>(igen)ectorE, identiCying sbgro!s e.g.,"et#ork>Begions> o4!onents, "et#ork>Begions>VNore,"et#ork>%bgro!s>liGes, "et#ork>%bgro!s>actionsE andlocating strctrally eGi)alent actors e.g.,

59+ersion 1.0el!>el! To!ics 2ntrodction %ection%tandard Datasets el!>anne4an Ttorial/!tions >el!er &!!lications"et#ork>Boles and ositions>%trctral and "et#ork>Boles andositions> &to4or!$icE.

O4!ing o)er to t$e el! 4en, t$e el!>el! To!ics co44andleads sers to its H/)er)ie# oC el!I Cnction. T$e H2ntrodction%ectionI link !ro)ides access to a series oC $el! to!ics t$atco)ers 4ost bt not allE oC 72"(TAs Cnctions #$en ne#Cnctions are added to 72"(T, it so4eti4es takes a#$ile beCoret$ey are co)eredE. T$e H/)er)ie# oC el!I Cnction also !ro)idesa H%tandard DatasetsI link t$at !ro)ides sers #it$ a brieCdiscssion oC all t$e social net#ork datasets t$at co4e #it$72"(T. inally, t$e el!>anne4an Ttorial co44and links sersto t$e )ery $el!Cl 72"(T gide #ritten by anne4an and Biddle300E.

T$e +isalize 4en !ro)ides sers #it$ access to t$ree)isalization !rogra4s "etDra#, a8ek and :age. Fe #ill only se"etDra# and a8ek in t$is gide alt$og$ it is #ort$ 4entioningt$at beCore t$e ad)ent oC a8ek and "etDra#, :age #as t$e !rogra4oC c$oice Cor 4any social net#ork analysts ree4an 1;;;, 3000L

ree4an, Febster and Virke 1;;E. :age #as initially de)elo!ed asa de)ice to be sed in 4oleclar 4odeling Bic$ardson andBic$ardson 1;;3E, bt social net#ork analysts Cond it attracti)ebecase it !rodces elegant t$reeNdi4ensional interacti)e i4ages.2n :age researc$ers can rotate i4ages, trn !arts oC t$e dis!layoCC and on, se t$e co4!ter 4ose to select and identiCy )arios!arts oC t$e net#ork, and ani4ate c$anges bet#een diCCerentarrange4ents oC ob8ects.

6enerally, yo #ill #ant to lea)e t$e deCalt settingsinclded nder t$e /!tions 4en ntoc$ed. T$e one e@ce!tion tot$is rle is t$e /!tions>el!er &!!lications co44and. licking on

t$is co44and brings ! t$e Collo#ing dialog bo@ igre 5.9, ne@t!ageE. &s yo can see t$is allo#s sers to c$ange t$e Colders#$ere t$e Cor $el!er a!!lications crrently incor!orated by72"(T "etDra#, a8ek, :age and "ote!adE. $ances are yo #illne)er need to tell 72"(T to look Cor "etDra# and "ote!ad in adiCCerent Colder t$an t$e deCalt Colders set by 72"(T. o#e)er,yo #ill !robably #ant to c$ange #$ere 72"(T looks Cor a8ekand !er$a!s :ageE Cor t$e si4!le reason t$at t$e )ersion oC


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a8ek and :ageE distribted by 72"(T is ty!ically not t$e 4ostrecent )ersion. Wo #ill #ant to do#nload and install a8ek inits deCalt location i.e., \!a8ek\a8ek\ a8ek.e@eE. %o beCoredoing anyt$ing else, click on t$e radio btton to t$e rig$t oCt$e a8ek !rogra4 location circled in igre 5.9 abo)e, and

c$ange a8ekAs deCalt location to \!a8ek\a8ek\[email protected] t$is #ill insre t$at eac$ ti4e yo o!en a8ek Cro4 #it$in72"(T yo #ill o!en t$e 4ost recent )ersion ass4ing, oCcorse, t$at yo !date a8ek on a reglar basisE.5+ersion 1.0ocate el!er &!!lications

"etDra# !rogra4 0V

``''rogra4 iles\&nalytc Tec$nologies\"elDra)&"etdra#.e@e ancel

a8ek !rogra42 ''rogra4 iles\&naly tic Tec$nologes\ el!er &!!s\!a8ek.e@e C 8 O :age !rogra4`''rogra4 iles\&nalytc Tec$nologies\ el!er &!!s\4age.e@eTe@t editor1 note!ad.e@e ... `

1igre 5.9 72"(T el!er &!!lication Dialog -o@

2t is no# ti4e to trn or attention to "etDra#, a net#ork

)isalization !rogra4 t$at integrates nicely #it$ 72"(T. -ecase#e #ill o!en "etDra# Cro4 #it$in 72"(T, t$ere is no need toclose 72"(T at t$is ti4e.5.3 "etDra#

2n recent years social net#ork analysts $a)e begn sing aseries oC 4at$e4atical tec$niGes to locate a social net#orkAsactors in sc$ a #ay t$at t$e distances bet#een t$e4 are4eaningCl. T$ese algorit$4s se t$e conce!ts oC s!ace anddistance in order to re!resent a net#orkAs internal strctre,#$ic$ t$ey $o!e #ill re)eal, a4ong ot$er t$ings, #$ic$ actors areHcloseI to one anot$er and #$et$er !otential clea)ages e@istbet#een sets oC actors. "etDra# is !rogra4 de)elo!ed by one oC72"(TAs creators %te)e -orgattiE t$at is designed to dra#net#orks sing so4e oC t$ese algorit$4s. "et#ork 4a!s created by"etDra# can be rotated, Cli!!ed, resized and stored in se)eraldiCCerent Cor4ats is4an and )an Di8n 30050


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F$ile tec$nically a standNalone !rogra4, "etDra# essentiallyCnctions as an e@tension oC 72"(T it is distribted #it$72"(T, it can be o!ened Cro4 #it$in 72"(T, and it reads 72"(TCiles #it$ot t$e need Cor sing any i4!orting andKor e@!ortingCnctions is4an and )an Di8n 30050/!en>7cinet dataset>


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"et#ork co44and. T$is s$old yield an initial net#ork 4a! t$atlooks si4ilar to t$e one dis!layed in igre 5.< belo#5=+ersion 1.0S"etDra#]

ro!erties>ines>olor>Belation

igre 5.olor>Belation igre 5.=, ne@t !ageE. "otet$at "etDra# ato4atically assigns colors to t$e diCCerent ty!esoC ties. Wo can c$ange t$ese deCalts by clicking on t$e colorbo@. 6enerally, $o#e)er, t$ose c$osen by "etDra# tend to !ro)idea nice contrast bet#een t$e ty!es oC ties, so it is ad)isable toat least begin #it$ t$e deCalt colors. Wo can al#ays c$anget$e4 later. "ote also t$at #$en t#o actors s$are 4ore t$an one


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tie, "etDra# colors t$ese relations$i!s gray. Wo can c$ange t$isdeCalt as yo do t$e ot$ers by clicking on t$e color bo@. /nceyo select H&!!lyI "etDra# assigns t$e diCCerent colors to t$ediCCerent ty!es oC ties. T$ere are ot$er #ays to color relationsin "etDra#, bt t$is see4s to be t$e 4ost stable a!!roac$ at

least Cor no#E.5+ersion 1.0ayot>ircleayot>Bando4

igre 5.= "etDra#As Holor ines by BelationI Dialog -o@:a!!ing &lgorit$4s in "etDra#

%ocial net#ork analysts $a)e long sed net#ork 4a!s to)isalize social net#orks. & co44on tec$niGe in t$e early daysoC social net#ork analysis #as to constrct t$e data arond t$ecirc4Cerence oC a circle. "etDra# incldes a co44and t$atcreates t$is ty!e oC net#ork 4a! ayot>ircle. 7nCortnately,#$ile t$is a!!roac$ can 4ake t$e strctre oC relations clearer,t$e relations bet#een t$e gra!$As !oints do not reClect anys!eciCic 4at$e4atical !ro!erties.

T$e !oints are arranged arbitrarily, and t$e distances bet#eent$e4 are 4eaningless, #$ic$, de!ending on $o# t$ey #ere arranged,can lead to )arying inter!retations oC t$e data :c6rat$, -lyt$eand Vrack$ardt 1;;=E. "etDra# also incldes an algorit$4 t$atrando4ly allocates a net#orkAs nodes ayot> Bando4E, bt t$isty!e oC layot sCCers Cro4 t$e sa4e #eaknesses as does acirclar layot t$e distances bet#een t$e gra!$As nodes 4eannot$ing.


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2n recent years analysts $a)e begn sing a series oC4at$e4atical tec$niGes to locate t$e !oints oC a net#ork in sc$a #ay t$at t$e distances bet#een t$e4 are 4eaningCl.:ltidi4ensional scaling :D%E is one sc$ tec$niGe. 2t ses t$econce!ts oC s!ace and distance to re!resent a net#orkAs internal

strctre, #$ic$, in trn, can $el! re)eal, a4ong ot$er t$ings,#$ic$ actors are HcloseI to one anot$er or !otential clea)agesbet#een sets oC actors Fasser4an and ast 1;;9E. T$e ty!icalin!t to :D% is a oneN4ode sy44etric5;+ersion 1.04atri@ consisting oC 4easres oC si4ilarity or dissi4ilaritybet#een !airs oC actors. /t!t generally consists oC a set oCesti4ated distances a4ong !airs oC actors t$at can be t$enre!resented in oneN, t#oN, t$reeN or $ig$erNdi4ensional s!aceVrskal and Fis$ 1;=L Fasser4an and ast 1;;9E.

T$ere are diCCerent ty!es oC 4ltidi4ensional scaling 4etric:D% and non4etric :D%. :etric :D% takes a gi)en 4atri@ oC!ro@i4ities t$at 4easre t$e si4ilarities or dissi4ilaritiesa4ong a set oC actors and calclates a set oC !oints in kNdi4ensional s!ace, sc$ t$at t$e distances bet#een t$e4corres!ond as closely as !ossible to t$e in!t !ro@i4ities.:etric distance diCCers Cro4 distance in gra!$ t$eory. 2n gra!$t$eory, t$e distance bet#een t#o !oints is 4easred in ter4s oCt$e n4ber oC lines in t$e !at$ t$at connects t$e t#o !oints. 2n:D% t$e distance bet#een t#o !oints is t$e 4ost direct rotebet#een t$e4. H2t is a distance t$at Collo#s a rot Zas t$e cro#CliesA, and t$at 4ay be across Zo!en s!aceA and need not N

indeed, it nor4ally #ill not N Collo# a gra!$ t$eoretical !at$I%cott 300019N19;E.

T$ere are so4e li4itations to sing 4etric :D% Cor )isalizingsocial net#orks. :any net#orks are binary i.e., dic$oto4osE inCor4. T$ey si4!ly indicate eit$er t$e !resence or absence oC atie, #$ic$ 4eans t$at #e cannot directly se sc$ data to 4easre!ro@i4ities. 2nstead, #e need to Cirst con)ert it into ot$er4easres, sc$ as correlation coeCCicients, beCore calclatingits 4etric !ro!erties. o#e)er, sc$ data con)ersion can leadresearc$ers to dra# n8stiCiable conclsions abot t$e data. ore@a4!le, #$ile it is reasonable to ass4e t$at an actor #it$ Cor

ties is 4ore central t$an one t$at $as only t#o, bt #e cannot becertain t$at t$e Cor4er is t#ice as central as t$e latter %cott30001=E. ()en #$en t$e data are )aled, 4etric ass4!tions 4aybe ina!!ro!riate. 24agine t#o actors #it$ Cor ties bet#een t$e4and t#o ot$er actors #it$ only one. F$ile t$e Cirst set oC actorsis al4ost certainly 4ore closely tied t$an t$e second set, againit is diCCiclt to kno# $o# 4c$ 4ore closely tied toget$er t$eyare %cott 30001=E.


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"onN4etric :D% !rocedres oCCer a soltion to t$is !roble4.ike 4etric :D% !rocedres, t$ey se sy44etrical ad8acency4atrices in #$ic$ t$e cells reClect t$e si4ilarities ordissi4ilarities a4ong actors, bt nlike 4etric :D% !rocedres,t$ey treat t$e data as ordinal data, seeking Ha soltion in #$ic$

t$e rank ordering oC t$e distances is t$e sa4e as t$e rankordering oC t$e original)alesI %cott 30001=E. :oreo)er, non4etric :D% is oCten!reCerred becase it13tends to !ro)ide a better HgoodnessNoCNCitI stressE statistic.13T$e lo#er t$e stress 0 !erCect CitE, t$e better. 6enerally,stress le)els belo# H. 1I are considered e@cellent #$ile le)elsabo)e .3 are considered nacce!table.90+ersion 1.0ayot>6ra!$ T$eoretic layot>:D%ayot>6ra!$ T$eoretic layot >6o#erayot>6ra!$ T$eoretic layot >%!ring e4bedding

rrently, "etDra# only incldes 4etric :D% algorit$4salt$og$ !lans Cor15nonN4etric :D% algorit$4s are in t$e #orks.24!le4enting"etDra#As 4etric :D% rotine is relati)ely straig$tCor#ard.

%i4!ly isse "etDra#As ayot> 6ra!$ T$eoretic layot>:D% co44andor click on its :D% s!eed bttonE and obser)e t$e c$ange in t$edra#ing. "odes t$at are HsociallyI close to one anot$er becaset$ere is a tie bet#een t$e4 or t$ey are tied to a co44on CriendEs$old be located close to one in t$e gra!$, #$ile nodes t$at aresocially distant Cro4 one anot$er i.e., t$ey are not tied to oneanot$er nor do t$ey s$are a tie to co44on tieE s$old be locatedCar Cro4 one anot$er in t$e gra!$. 2t is i4!ortant to note t$att$ere is no single correct #ay to gra!$ t$e data i.e., t$ere isnot a single HsoltionE, #$ic$ is #$y analysts #ill generally#ant to i4!le4ent an algorit$4 or )arios algorit$4sE 4lti!le

ti4es. &not$er 4etric :D% algorit$4 inclded in "etDra# is t$eayot>6ra!$ T$eoretic layot>6o#er co44and or click on t$e 6s!eed bttonE. "ote t$at all oC t$ese rotines !ro)ide a slig$tlydiCCerent net#ork 4a! Cro4 one anot$er, #$ic$ 4akes it diCCicltto c$oose #$ic$ net#ork 4a! best Cits t$e data. &n alternati)e isto calclate t$e coordinates in 72"(T and t$en i4!ort t$e4 into"etDra# see &!!endi@ 5E. T$e ad)antage is t$at 72"(TAs :D%rotines not only allo# sers to c$oose bet#een 4etric and


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non4etric algorit$4s, bt t$ey also !ro)ide sers #it$ a stressstatistic t$at indicates $o# #ell t$e coordinates Cit t$e data.

&not$er !o!lar set oC rotines Cor gra!$ing social net#orksare s!ringN e4bedded algorit$4s. a8ek, in Cact, only sess!ringNe4bedded algorit$4s. %!ringNe4bedding algorit$4s treat t$e

nodes as !s$ing and !lling on one anot$er and seek to Cind ano!ti44 soltion #$ere t$ere is a 4ini44 a4ont oC stress on t$es!rings connecting t$e #$ole set oC nodes ree4an 3000E.6enerally ties bet#een nodes are treated as an attracti)e Corcea Zs!ringA !lling t$e4 toget$erE #$ile nodes t$at do not s$area tie are !s$ed a!art :oody 3001E. T$e s!ringNe4beddingalgorit$4 in "etDra# can be i4!le4ented sing t$e ayot>6ra!$T$eoretic layot>%!ring e4bedding co44and. T$is brings ! adialog bo@ not s$o#nE t$at !ro)ides yo #it$ a )ariety oCo!tionsKcriteria Cor sing t$e s!ring e4bedding layot.6enerally, it is a good idea to se "etDra#As deCalts alt$og$)arying t$e o!tions tends not to c$ange t$e gra!$As layot toodra4atically. T$e lig$tening bolt s!eed btton is anot$er #ay toi4!le4ent t$is rotine, #$ile t$e lig$tening bolt !ls eGalssign btton i4!le4ents a )ariation on t$e s!ring e4beddingrotine.15%ee t$e o!tions Cond nder t$e ayot>%calingK/rdinationsb4en N only t$e 2terati)e 4etric :D% algorit$4 $as beeni4!le4ented and !rodces a )ery diCCerent soltion t$an t$e ot$er:D% rotines Cond in "etDra#. 7sers can calclate 4etric andnon4etric :D% coordinates in 72"(T and t$en se t$esecoordinates in "etDra#, $o#e)er. %ee &!!endi@ 5 Cor details.91

+ersion 1.0ayot>6ra!$ T$eoretic layot >rinci!al o4!onentsro!erties>"odes>%y4bols>olor>&ttribteNbased

"etDra# oCCers one additional layot algorit$4 N rinci!alo4!onents analysis so4eti4es reCerred to as Cactor analysisE,#$ic$ ty!ically !ro)ides a diCCerent and oCten 4ore Hdra4aticIgra!$ oC t$e net#ork in t$at si4ilar nodes tend to clster 4oretig$tly toget$er. "etDra# i4!le4ents its rinci!al o4!onentsalgorit$4 sing t$e ayot>6ra!$ T$eoretic layot>rinci!al

o4!onents co44and or t$e s!eed bttonE. T$e logic be$ind!rinci!al co4!onents CactorE analysis is so4e#$at diCCerent t$ant$e ot$er a!!roac$es. 2t is a 4et$od Cor co4bining correlatedactors into a s4aller n4ber oC nderlying di4ensions. T$ealgorit$4 searc$es Cor t$e 4ost $ig$ly correlated set oC actorsin t$e net#orkL t$is beco4es t$e Cirst co4!onent. 2t t$ensearc$es Cor a second set oC actors t$at is ncorrelated #it$ t$eCirst, #$ic$ beco4es t$e second co4!onent. -ecase t$ey are


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ncorrelated #it$ one anot$er i.e., becase t$ey are ort$ogonal#it$ one anot$erE t$ey Hcan be dra#n at rig$tNangles to oneanot$er as t$e a@es oC a t#oNdi4ensional scatter diagra4I %cott300019E. 2n order Cor a rinci!al o4!onents layot to beconsidered a seCl 4a! oC a net#ork, t$e Cirst t#o di4ensions

or t$ree iC yo are #orking #it$ a t$reeNdi4ensional layotE4st accont Cor a sbstantial a4ont oC t$e )ariance in t$eoriginal data. 2C t$ey do not, t$en anot$er ty!e oC layot is inorder. 7nCortnately, as oC no# "etDra#As rinci!al o4!onentsrotine does not tell s $o# 4c$ oC t$e )ariance in t$e originalit Cor #$ic$ it acconts. T$s, analysts #ill need to relyso4e#$at on t$eir intition.Forking #it$ &ttribtes in "etDra#

&not$er nice Ceatre oC "etDra# is t$at it allo#s analysts toincor!orate attribte data into its net#ork gra!$s. To get asense oC t$is, o!en t$e attribte Cile ig$NTecN&ttribtes.[[$Eassociated #it$ t$e Vrack$ardt net#ork data #$ic$ s$old stillbe loaded into 4e4oryE, sing t$e ile>/!en>7cinet dataset>&ttribte data co44and. F$en yo click /V, a node attribteeditor s$old a!!ear not s$o#nE t$at is si4ilar to as!reads$eet. lose it by clicking on t$e red HXI in t$e !!errig$t corner. et s Cirst c$ange t$e color oC t$e nodesKactorsto reClect t$e de!art4ent to #$ic$ t$ey belong. To do t$is isset$e ro!erties> "odes>%y4bols>olor>&ttribteNbased co44and,#$ic$ s$old bring ! a dialog bo@ si4ilar to t$e one in igre5.. 7sing t$e dro!Ndo#n bo@ circled in igre 5. belo#E c$ooset$e attribte yo #is$ to se to color t$e node in t$is caseHD(TIE and notice t$e c$ange in t$e color oC t$e nodes.19

19&s beCore "etDra# ato4atically assigns colors Cor t$e )ariosde!art4ents to #$ic$ t$e 4anagers belong.93+ersion 1.0ro!erties>"odes>%y4bols >%ize >&ttribteNbased

igre 5. "etDra#As Holor "odes by olorI Dialog -o@


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igre 5.; "etDra# :a! oC Vrack$ardt Data #it$ olor and %izeBeClecting &ttribtesWo can )ary t$e size and s$a!e oC t$e nodes as #ell sing t$e

ro!erties> "odes>%y4bols>%ize>&ttribteNbased andro!erties>"odes>%y4bols>%$a!e> &ttribteNbased co44andsres!ecti)ely. Try ad8sting t$e size oC t$e nodes based ontenre. Wo s$old get a net#ork gra!$ t$at looks so4e#$at

si4ilar to t$e one abo)e igre 5.;E. &s yo can see lengt$ oCtenre does not a!!ear to corres!ond #it$ centrality in t$enet#ork.95+ersion 1.0ile>%a)e Data &s >a8ek>"et ile5.5 a8ek

a8ek N #$ic$ 4eans Hs!iderI in %lo)enian N #as created by+ladi4ir -atagel8 and &ndre8 :r)ar in 1;;< and is designed to$andle )ery large datasets %cott 30001=;N10E. F$ile it doesnot oCCer as 4any social net#ork rotines as does 72"(T e.g.,

it only co4!tes degree, closeness and bet#eenness centralityE,it still oCCers 4ost oC t$ose t$at analysts se. 2n !articlara8ek tends to inclde rotines t$at lend t$e4sel)es to t$e)isalization and si4!liCication oC large social net#orksis4an and )an Di8n 30030E. a8ek rns on Findo#sNco4!atible co4!ters, can be do#nloaded Cor Cree and isconstantly being !dated by its de)elo!ers. a8ek ses si@


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diCCerent ty!es oC data ob8ects or strctres is4an and )anDi8n 30031EJ "et#orks nodesKactors and tiesEJ artitions discrete classiCication oC nodes #$ere eac$ node is

assigned to one and only one class N Cor e@a4!le, a dark

net#ork !artition 4ig$t assign eac$ actor to a s!eciCic roleEJ +ectors continos !ro!erties oC nodes N Cor e@a4!le, anactorAs age, le)el oC edcation, centrality score, etc.E

J er4tations reordering oC nodesEJ lsters sbsets oC nodesEJ ierarc$ies $ierarc$ically ordered clsters and nodesEFe #ill not e@!lore all oC t$ese data ob8ects o)er t$e corse oCt$is gide indeed, #e #ill tilize !ri4arily t$e Cirst t$ree Nnet#orks, !artitions and )ectorsE, bt it is $el!Cl to at leastbe a#are oC t$e4.

7nlike 72"(T, #$ic$ stores net#ork data as a 4atri@, a8ekstores net#ork data as an edge list, #$ic$ is si4!ly a list oC)ertices i.e., actorsKnodesE and edgesKarcs i.e., tiesE. igre5.10 belo#E dis!lays a !ortion oC t$e a8ek Vrack$ardt ig$ Tec$net#ork data Cile. T$e Cile begins by s!eciCying t$e n4ber oC)erticesL t$en eac$ )erte@ is identiCied on a se!arate line by aserial n4ber, a label enclosed in Gotation 4arksE and t#on4bers bet#een 0 and 1, #$ic$ are si4!ly t#o sets oC coordinatesCor )isalizing t$e net#ork data in t#oN

T$ere are a n4ber oC ot$er !rocedres a)ailable #it$in"etDra# t$at #e #ill consider later in t$e gide. "o# #e #illtrn or attention to a8ek. -eCore 4o)ing to a discssion oCa8ek, $o#e)er, #e need to Cirst sa)e t$e Vrack$ardt data in

a8ek Cor4at. To do t$is se "etDra#As ile>%a)e Data&s>a8ek>"et ile co44and. et s no# trn or attention toa8ek.99+ersion 1.0di4ensional s!ace. T$e list oC )ertices is t$en Collo#ed by alist oC arcs. (ac$ line identiCies t$e n4ber oC t$e sending)erte@, t$e n4ber oC t$e recei)ing )erte@ and t$e )ale oC t$etie. T$s, yo can see t$at t$e Cirst 4anager )erte@ 1E sog$tad)ice Cro4 4anagers 3, 9, , 1


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33

_.95_< . 9_9

5 5

0.=31< _.9=_=

9 '9

0.


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1 1 11 31 13 < 13 = 13 31 1

5 1 15 3 15 9 15 < 15 = 15 15 ; 15 10 1 +igre 5.10 a8ek "et ile (dge istE

/ne oC a8ekAs nicer Ceatres is t$at sers can load 4lti!lenet#orks and ot$er data ob8ects e.g., !artitionsE into 4e4ory att$e sa4e ti4e. T$is is Gite $el!Cl becase, like ot$er socialnet#ork soCt#are !rogra4s, 4ost oC a8ekAs rotines generate ne#net#orks or ot$er data ob8ectsE. &ll oC t$ese can t$en be storedin #$at a8ek calls a H!ro8ect Cile,I #$ic$ 4eans t$at aCteranalyzing one or 4ore social net#orks, sers can sa)e all oCt$eir #ork in a single Cile. T$is decreases t$e likeli$ood t$atsers #ill $a)e to later Hrecreate t$e #$eelI in doing t$eiranalysis.

a8ekAs !ri4ary #eakness is t$at it only contains Ce#er socialnet#ork !rocedres t$an 72"(T alt$og$ it does inclde a Ce#t$at 72"(T does not $a)eE, and t$e net#ork 4ani!lation Ceatresare so4e#$at li4ited. T$at is #$y

9+ersion 1.0ile>"et#ork>Beada8ek>Dra# >Dra#4any analysts so4eti4es se 72"(T Cor data 4ani!lation and t$entrn to a8ek Cor )isalization !r!oses. To a8ekAs credit,$o#e)er, it no# allo#s sers to call t$e statistical !ackages HBIand H%%%I to !erCor4 statistical !rocedres not a)ailable ina8ek.6etting %tarted #it$ a8ek

T$e a8ek 4ain 4en screen looks )ery diCCerent Cro4 t$at oC

72"(T and "etDra# see igre 5.11 belo#E. &s yo can see it isorganized by t$e ty!e oC data ob8ect or strctre discssedabo)e. &nd, like 72"(T and "etDra# it incldes a n4ber oCdiCCerent 4ens Cor 4ani!lating and analyzing data.a8ek 00iles /!erations artition artitions +ector


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"et"el

+ectors er4tation er4tations lsterierarc$y /!tions Dra# :acro 2nCo Tools

"elFoiks

e

22 d

Rl4ions

1 d

edClf+ectors

1 d

e8ClO9

11 reiiiiiiiiins 11 1a 1 1U1

7 sinrO^2:

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ierarc$y

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igre 5.11 a8ek :ain :enTo o!en a a8ek Cile, se t$e a8ekAs ile>"et#ork>Bead

co44and or click on t$e Colder icon located nder t$e H"et#orksIbtton circled in igre 5.11E. T$is brings ! a dialog bo@ nots$o#nE t$at looks Cor diCCerent ty!es oC Ciles. -e sre t$atHile Ty!eI reads Ha8ek net#orks *.netEIL ot$er#ise yo #illnot be able to Cind t$e net#ork data #e 8st sa)ed in "etDra#."ote t$at a8ek loads t$e net#ork in t$e net#ork dro!do#n listnot s$o#nE.1 To )ie# t$e net#ork, se t$e a8ek>Dra#>Dra#co44andL t$is o!ens a8ek dra# screen, #$ic$ #ill look so4et$inglike igre 5.13


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1&lt$og$ it is not ob)ios Cro4 t$e dro!do#n list, "etDra#only sa)ed t$e Cirst net#ork oC t$e Vrack$ardt data t$e ad)icenet#orkE, #$ic$ 4eans t$at in a8ek #e #ill only be able to lookat t$e Cirst net#ork. T$ere is a #ork arond Cor t$is, bt #e#ill take t$at ! later in t$e gide.

9olor >-ackgrond/!tions>+ale oC ines >%i4ilaritiesayot>(nergy >%tarting ositions >6i)en @y

( 1. \rogra4 iles\&nalytic Tec$nologies7Ocinetolor>-ackgrond co44and. T$is brings ! a dialog bo@s$o#ing a n4ber oC colors Cro4 #$ic$ to c$oose. %elect t$ebackgrond oC yor c$oice. "e@t, yo #ill generally #ant to tella8ek t$at ties bet#een actors indicate si4ilarities or closenessbet#een t$e4. To do t$is se t$e /!tions>+ales oCines>%i4ilarities co44and. inally, select t$eayot>(nergy>%tartingositions>6i)en @y i.e., $orizontal and)ertical di4ensionsE o!tionL t$is insres t$at #it$ eac$ ne#dra#ing a8ek begins #it$ t$e nodesKactors #$ere t$ey are aso!!osed to rando4ly !lacing t$e4 beCore dra#ing t$e net#ork 4a!E

and ass4es t$at re!eated dra#ings oC net#orks yield a bettersoltion:a!!ing &lgorit$4s in a8ek

&s noted abo)e a8ek only ses s!ring e4bedding algorit$4s Corits layots. 2n !articlar it ses t#o rc$ter4an Beingold andVa4ada Va#ai. T$e Va4ada and Va#ai 1;;E algorit$4 is based onan ass4ed attraction bet#een ad8acent !oints i.e., actors t$atare tied #it$ one anot$erE and an ass4ed re!lsion bet#een nonN


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ad8acent !oints i.e., actors t$at are not tied to one anot$erEand allocates !oints in t#oNdi4ensional s!ace. T$e rc$ter4anand Beingold 1;;1E algorit$4 is si4ilar to t$e Va4adaNVa#aialgorit$4, bt rat$er t$an ass4ing attraction bet#een ad8acent!oints and re!lsion bet#een nonNad8acent !oints, it

9=+ersion 1.0SDra# %creen] ayot>(nergy >rc$ter4an Beingold >3D, 5Dayot>(nergy>Va4adaNVa#ai>reeSDra# %creen]Dra#>2nCoDra#>2nCo >losest +erticesS72"(T] Data>(@!ort>a8ek >ategorical &ttribteatte4!ts to si4late a syste4 oC 4ass !articles #$ere t$e)ertices si4late 4ass !oints re!elling eac$ ot$er #$ile t$eedges si4late s!rings #it$ attracting Corces. 2t t$en tries to4ini4ize t$e HenergyI oC t$is !$ysical syste4. To i4!le4entrc$ter4an Beingold, se a8ekAs ayot>(nergy>rc$ter4anBeingold>3D, 5D co44andL to i4!le4ent Va4ada Va#ai, se itsayot>(nergy>Va4adaN Va#ai>ree co44and.

F$ic$ one s$old yo c$oose? /n t$e one $and t$e Va4adaNVa#aialgorit$4 #orks #ell #it$ s4all, connected net#orks bt is notreco44ended Cor net#orks #it$ 4ore t$an 00 )ertices de "ooy,:r)ar and -atagel8 3001=E. 2t dra#s layots si4ilar tonon4etric :D% and tends to be better t$an rc$ter4an Beingold at4a!!ing s!arse net#orks. 7nCortnately, it !laces isolated nodesrando4ly on t$e gra!$, so t$ey can so4eti4es a!!ear to be in t$e

center oC a net#ork #$en in reality t$ey are not. /n t$e ot$er$and, t$e rc$ter4an Beingold algorit$4 is Caster and #orks #ell#it$ large net#orks. 2t also is able to distribte !oints in bot$t#oNdi4ensional and t$reeNdi4ensional s!ace. 6enerally, it is agood idea to Cirst )isalize t$e net#ork sing rc$ter4anBeingold, and t$en aCter 4aking sre t$at t$eayot>(nergy>%tarting ositions>6i)en @y o!tion $as beenselectedE 4o)e to sing Va4adaNVa#ai.

7nCortnately, a8ek does not !ro)ide goodness oC Citstatistics Cor net#ork 4a!s, #$ic$ 4akes it 4ore diCCiclt Coranalysts to ob8ecti)ely e)alate t$e accracy oC a net#ork 4a!.

a8ek does, $o#e)er, e)alate t$e est$etic !ro!erties oC anet#ork dra#ing #it$ t$e series oC co44ands Cond nder t$eDra#>2nCo sb4en. or e@a4!le, so4e arge t$at t$e n4ber oCcrossing lines in a gra!$ s$old be ke!t to a 4ini44 and t$atnconnected )ertices s$old not be dra#n too closely to oneanot$er de "ooy, :r)ar and -atagel8 3001E. %o, iC yo selectt$e Dra#>2nCo>losest +ertices co44and, a8ek identiCies t$enodes i.e., )erticesE t$at !erCor4 t$e #orst on t$is as!ect oC


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gra!$ dra#ing and gi)es t$e4 a diCCerent color, 4aking t$e4 easyto identiCy. Wo can t$en se t$e 4ose to drag t$e t#o )erticesCart$er a!art Cro4 one anot$er.Forking #it$ &ttribtes in a8ek

Fe #ill no# look at $o# to #ork #it$ attribte data in a8ek.

2n order to do t$is, #e need to Cirst e@!ort t$e Vrack$ardtattribte data Cro4 72"(T as a8ek !artitions and )ectors. 2n72"(T se 72"(TAs Data>(@!ort>a8ek> ategorical &ttribteco44and, #$ic$ brings ! t$e Collo#ing dialog bo@9+ersion 1.0S72"(T] Data>(@!ort>a8ek >antitati)e &ttribteSa8ek] ile >artition >Bead(@!ort alitati)e &ttribtes to a8ek .cl Ciles2n!tE N &ttribte datasetDatailes\ig$NTec&ttiibtes.tttt$ ...

\y 7Vi

"o. oC deci4al !laces 1^Xancel

/t!t CileCs8 !reCi@ `&to4atic ...`

= el!igre 5.15 72"(TAs (@!ort alitati)e &ttribte Data to a8ekDialog -o@%elect t$e Hig$NTecN&ttribtes.[[$I Cile and click /V. T$is #illcreate Cor !artition Ciles, one Cor eac$ ty!e oC attribte.Tec$nically, not all oC t$e ig$ Tec$ attribtes are !artitionsLinstead, t$ey are )ectors. Becall Cro4 t$e discssion abo)e t$at

a a8ek !artition assigns eac$ node to one and only one class. 2nter4s oC t$e Vrack$ardt data, t$e de!art4ent attribte Cile Citst$is descri!tion. T$e data are not ordered bt t$ey can beE andeac$ 4anager is only belongs to one de!art4ent. T$e ot$erattribte data age, le)el and tenreE are better t$og$t oC as)ectors becase t$ey re!resent continos data, so #e s$olde@!ort t$ese data sing 72"(TAs Data>(@!ort>a8ek>antitati)e&ttribte co44and. T$is #ill bring ! a dialog bo@ si4ilar toigre 5.19. /nce again select t$e Hig$N TecN&ttribtes.[[$ICile and click /V. &s beCore t$is co44and #ill create Cor Ciles,one Cor eac$ attribte, e@ce!t t$at t$is ti4e t$ey #ill $a)e a

.)ec e@tension./r ne@t task is to i4!ort t$e attribte Ciles into a8ek.

irst, se a8ekAs ile>artition>Bead co44and or click on t$eColder icon nder t$e HartitionI bttonE in order to i4!ort t$eD(T.cl Cile see igre 5.19E


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igre 5.1 a8ekAs Bead artition Dialog -o@9;+ersion 1.0ile> +ector>BeadDra#>Dra#NartitionN+ectorSDra# %creen] /!tions>%ize >oC +ertices"e@t, se a8ekAs ile>+ector>Bead co44and or click on t$eColder icon nder t$e H+ectorI bttonE to i4!ort t$e age, le)eland tenre )ectors dialog bo@ not s$o#nE. Wo $a)e to read ineac$ )ector se!arately. Wo cannot read t$e4 in en 4asse. Fit$t$e Vrack$ardt net#ork $ig$lig$tedKselected in t$e "et#orkdro!do#n list i.e., dro! do#n 4enE, t$e de!art4ent !artition

$ig$lig$ted in t$e artition dro!do#n list and t$e tenre )ector$ig$lig$ted in t$e +ector dro!do#n list see igre 5.1< belo#E,select a8ekAs Dra#>Dra#NartitionN+ector co44and and energize itsing one or bot$ oC t$e )isalization algorit$4s.


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igre 5.1%ize>oC +ertices co44and in a8ekAs Dra# %creen. 2C yo ty!e int$e n4ber H0I, a8ek ato4atically ad8sts t$e size oC t$enodes. 2t is generally a good idea to let a8ek $a)e Cirst crackat esti4ating t$e size oC eac$ node. 2C t$ey are s4aller or

largerE t$an yo like, yo can al#ays ad8st t$e4 later. ere,t$e size $as been set to H5.I0+ersion 1.0


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igre 5.1= a8ekAs :ain %creen5.9 onclsion

2n t$is c$a!ter #e $a)e brieCly e@a4ined so4e oC t$e basicCeatres oC 72"(T, "etDra# and a8ek. &ll t$ree !rogra4s are#idely sed #it$in t$e social net#ork analysis co44nity. &llt$ree $a)e t$eir strengt$s and #eaknesses. 6enerally, analystsse 72"(T Cor esti4ating 4etrics and 4ani!lating data, "etDra#Cor t$e basic dra#ing oC social net#orks and a8ek Cor 4oreso!$isticated ty!es oC dra#ing social net#orks alt$og$ t$e lines

bet#een t$e t$ree are not Gite t$at clear ct.1+ersion 1.0&T(B96&T(B2"6, /(T2"6, :&"27&T2"6&"D+2%7&2M2"6%/2&"(TF/BVD&T& T(

-&%2%%ocial net#ork soCt#are !ackages sc$ as 72"(T, "etDra# and

a8ek oCten co4e #it$ readyNtoNse data. 2n t$e real #orld,$o#e)er, #e $a)e to collect and record or o#n data. Vno#ing $o#to do t$is is an i4!ortant Cirst ste! in social net#ork analysis.Fe can gat$er and !re!are social net#ork data in a )ariety oC

#ays, bt 4ost social net#ork analysts generally record socialnet#ork data in 4atri@ Cor4. or s4all datasets it is sallyeasiest to enter t$e data directly into 72"(T, sing itsinternal s!reads$eet Cnction. &n ad)antage oC entering socialnet#ork data into 72"(T is t$at #e can t$en get it into al4oste)ery ot$er social net#ork analysis !rogra4 since )irtally allread i.e., i4!ortE 72"(T datasets. &nd iC t$ey do not, 72"(Tis sally able to e@!ort t$e data in a Cor4at t$ey can read.


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7nCortnately, yo cannot record large social net#orks sing72"(TAs internal s!reads$eet becase oC col4n li4itations.:oreo)er, it can, at ti4es, be a bit Girky. T$at is #$y so4eanalysts !reCer to initially enter social net#ork data into astandard s!reads$eet !rogra4, sc$ as :icrosoCt (@cel, and t$en

ctting and !asting it into 72"(T. "ot only does (@cel not $a)et$e col4n li4itations oC 72"(TAs s!reads$eet, it is also 4orestable and incldes an HatoNco4!leteI Ceatre t$at co4!ares t$ete@t yo are ty!ing into a cell #it$ te@t already entered intot$e sa4e col4n, #$ic$ increases accracy e.g., consistentlys!elling t$e sa4e na4e t$e sa4e #ay eac$ ti4eE and in!t ti4e.1(@!ort>D

T$ere are 4lti!le 4et$ods Cor e@!orting oneN4ode socialnet#ork data toa8ek. T$e easiest, ass4ing t$at yo already $a)e t$e data in72"(T Cor4at, is1to si4!ly e@!ort t$e data Cro4 72"(T in a8ek Cor4.7nder t$eHDataI 4en, select t$e (@!ort>a8ek>"et#ork co44and note t$at72"(T !ro)ides a c$oice oC e@!orting t$e data in a n4ber oCCor4ats D, Vrack!lot, :age, a8ek, :etis, Ba#, and (@celE. T$isbrings a dialog bo@ igre 9.=, ne@t !ageE. 72"(T !ro)ides aseries oC o!tions alt$og$ 4ost oC t$e ti4e yo #ill #ant toacce!t 72"(TAs deCalt settings. & good rle oC t$4b is t$at iCyo do not kno# #$at t$e o!tion is asking, t$en acce!t 72"(TAsdeCalt "ote yo can click on t$e dialog bo@As el! btton Cora 4ore detailed discssion oC eac$ oC t$e o!tionsE.

T$e one e@ce!tion to t$e rle $ere concerns t$e Cinal o!tion,#$ic$ allo#s yo to lanc$ a8ek Cro4 #it$in 72"(T once t$e dataare e@!orted. Wo only #ant to se t$is o!tion iC 1E yo do notalready $a)e a8ek o!en and 3E yo $a)e set 72"(TAs o!tions so

t$at it #ill o!en t$e 4ost recent )ersion oC a8ek. /t$er#ise, it#ill lanc$ t$e )ersion oC a8ek t$at co4es #it$ 72"(T, #$ic$ isoCten so4e#$at dated. 2C yo c$oose yes, anot$er dialog bo@ #illa!!ear asking yo againE #$et$er yo #ant to lanc$ a8ek. 2Call goes #ell, 72"(T lanc$es a8ek #$en yo click t$e H/VIbtton. 2C not, yo can o!en a8ek and i4!ort t$e ne#ly createda8ek net#ork Cile 4anally.(@!ort to a8ekS2n!tE N"et#orkdataset

idin:O2"(T\iiends$i!Ties.tttt$

Dic$oto4ize)als > t$an 1Deleteisolates?

"o

S2n!t] Noordinatedataset 1S2n!t] N 1


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&ttribtedataset/t!t&ttribteCile

&to4atic

/t!tnet#orkCile

`riends$i!Ties.net

anc$ a8ekon e@it?

`Wes T

8a*X ancel ? Oel!igre 9.= 72"(T (@!ort to a8 ek Dialog -o@

-ecase a8ek no# allo#s sers to read in 4lti!le i.e.,stackedE net#orks see discssion in %ection 9.< belo#E, analysts4ay #ant to se 72"(TAs Data>(@!ort>D co44and #$en e@!orting4lti!le net#orks. Fe $a)e to se1or no#, 72"(T


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igre 9.Da)isAs%ot$ern lb Fo4en


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ST] 72"(T %!reads$eet N \Doc4ents and%ettings\%ean\Deskto!\DataW/!s3.[[$ile (dit TransCor4 ill abels /!tions el!

SD2^22%2 lX2CClal Ci 2 j.o` N.o i rm&strali...

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0 0 0 0

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&dng 0 0 0 o 8`8rrent cell Bo# olSQ STHDi4ensionsBo#s ols S=; S9C* "or4al %y44etricigre 9.; "oordin To!As /!erational "et#ork


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(@!orting T#oN4ode Data to a8ek7nCortnately, 72"(T TransCor4 >&rcs (dges>&ll

igre 9.10 72"(T (@!ort>D dialog bo@2t is !ossible t$at yo #ill get an error 4essage t$e Cirst ti4eyo click /V. 2t sally #orks t$e second ti4e, bt yo #ill!robably need to c$ange t$e e@tension to .dat again. "ote t$at#$en e@!orting t#oN4ode data, 72"(T does not !ro)ide a Hanc$a8ekI o!tion. T$s, yo #ill need to o!en a8ek se!arately and

read t$e net#ork 4anally.Farning (@!orting /ne and T#oN4ode Data to a8ek/ne t$ing to kee! in 4ind #$en e@!orting data Cro4 72"(T to

a8ek, regardless oC #$et$er yo se 72"(TAsData>(@!ort>a8ek>"et#ork co44and or its Data>(@!ort>D co44and,#$en a8ek reads t$e Cile into 4e4ory, it reads all ties as arcsnot edgesE. T$is is Cine #$en yo are #orking #it$ directionaldata, bt iC yo are #orking #it$ nondirectional data e.g.,


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"oordinAs To!As riends$i! net#orkE, yo #ill need to se a8ekAs"et> TransCor4>&rcs^ (dges>&ll co44and. T$is brings ! a dialogbo@ asking iC yo #ant to create a ne# net#ork. T$is is generallya good idea so t$at yo do not o)er#rite t$e original, so click/V. T$is brings ! anot$er dialog bo@ asking iC yo #ant to

re4o)e 4lti!le lines. %elect o!tion Ci)e single lineE and click/V. Wo s$old no# $a)e net#ork t$at consists only oC edges, notarcs.


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1&CCiliations co44and. T$is brings ! a dialog bo@

like t$e one illstrated in igre 9.15. or an actorNby actor4atri@, c$oose HBo#I in t$e HF$ic$ 4odeI o!tion since actors aregenerally listed in ro#sL Cor an e)entNbyN e)ent 4atri@, c$ooseHol4nI in t$e HF$ic$ 4odeI o!tion since e)ents aCCiliationsEare generally listed in col4ns.


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igre 9.15 72"(T &CCiliations dialog bo@-e sre to sa)e t$e Ciles H/t!t datasetIE nder diCCerent

Cile na4es, ot$er#ise iC yo deri)e bot$ an actorNbyNactor 4atri@and an e)entNbyNe)ent 4atri@, #$ic$e)er one yo deri)e last #illo)er#rite any ones yo deri)ed earlier.=0+ersion 1.0Data>Dis!lay

"et>TransCor4 >3N:ode to 1N:ode >Bo#s, ol4ns7nCortnately, a #arning bo@ does not a!!ear in 72"(T #$en yoare abot to o)er#rite an already e@isting Cile. Wo can dis!layt$e t#o ne#lyNcreated net#orks by eit$er c$oosing t$e Dis!layo!tion Cond nder t$e Data 4en or by clicking on HDI iconlocated 8st belo# 72"(TAs 4en bar.a8ek

Deri)ing oneN4ode net#orks Cro4 t#oN4ode net#orks in a8ek issi4!le, bt like in 72"(TE yo need to kno# #$ic$ actorsKe)entsare assigned to t$e ro#s and col4ns. To create an actorNbyNactorcoN4e4bers$i!E 4atri@ c$oose t$e Bo#s o!tion nder t$e

"et>TransCor4>3N:ode to 1N:ode sb4en ass4ing t$at t$at actorsa!!ear are listed in ro#sE. &Cter issing t$e co44and, t$e Be!ort#indo# #ill a!!ear. lose t$is and yo #ill see t$at a ne#net#ork a!!ears in t$e "et#ork dro! list. Be!eat t$e !rocedre,e@ce!t c$oose t$e ol4ns o!tion.tel 72"(T %!reads$eet N \Doc4ents and %ettings\%ean\Deskto!\Data\&ttri btes.ile (dit TransCor4 ill abels /!tions el! 2^V-2%2(li4sllill ill .0 N.0 ieri

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2ndonesia

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Di4ensionsBo#s ols S=; Spq* "or4al %y44etricigre 9.15 "oordin &ttribte Data &ttribte Data

&s #e discssed in t$e second c$a!ter, alt$og$ social net#orkanalysis Cocses !ri4arily on t$e !attern oC ties bet#een actors,it does not ignore actors attribte data. Becording attribtedata in 72"(T is relati)ely straig$tCor#ard.=1+ersion 1.0S72"(T]Data>Dis!layigre 9.19 !re)ios !ageE dis!lays attribte data related to"oordinAs "et#ork. &s yo can see, t$e na4es oC actors a!!ear in


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ro#s #$ile t$e )arios ty!es oC attribtes a!!ear in col4ns.T$ese data diCCer Cro4 social net#ork data in t$at eac$ col4ncontains selCNcontained. or e@a4!le, t$e se)ent$ col4nindicates t$e )arios roles t$at indi)idals #it$in "oordinAsnet#ork Cilled #it$ eac$ n4ber indicating a diCCerent role.

/b)iosly, #it$ot a code book see &!!endi@ 1E, t$ere is no #ayto kno# #$at eac$ oC t$e )arios n4bers 4ean. Fe can seattribte data in )arios #ays, so4e oC #$ic$ #e #ill e@!lorelater in t$e gide. or no#, it is only necessary to de4onstrate$o# it is recorded.9.< &ggregating "et#orks :atricesE

7! to t$is !oint #e $a)e Cocsed on single ty!es oCrelations$i! a4ong actors Criends$i!, kins$i!, o!erations, etc.2n t$e real #orld, $o#e)er, actors are ty!ically in)ol)ed in 4oret$an one ty!e oC relation anne4an and Biddle 300E. &s #e $a)ealready seen $a!ter 1E, 4ost indi)idals are e4bedded in an4ber oC ty!es oC ties e.g., Criends$i!, kins$i! and econo4icE,and cor!orate and state actors are no diCCerent. -sinessesengage in Cinancial and inCor4ational e@c$anges and so4eti4esCor4 alliances #it$ one anot$er %a@enian 1;;9E, #$ile contriesare linked t$rog$ n4eros cltral, econo4ic, 4ilitary and!olitical ties not to 4ention transnational cor!orations,nongo)ern4ental organizations and international agencies :eyeret al. 1;;=E. :ore i4!ortantly Cor or !r!oses, diCCerent tiesoCten !s$ and !ll actors in diCCerent directions %i44el S1;0,1;33] 1;E. T$s, coding 4lti!le relations is es!eciallyi4!ortant. 72"(T incldes a )ariety oC tools Cor analyzing4lti!le@ data. %o4e allo# yo to re4o)e indi)idal 4atrices Cro4

a 4lti!le 4atri@ Cile, #$ile ot$ers allo# yo to create stackedsocial net#ork data Cro4 se!arate single social net#ork dataCiles.:lti!le Belations in 72"(T and "etDra#

/ne oC t$e 4ost co44on #ays oC storing 4lti!le@ data is byHstackingI a set oC actorNbyNactor 4atrices, one Cor eac$ ty!e oCrelation. igre 9.15 ne@t !ageE dis!lays !art oC t$e ot!tCro4 a Data>Dis!lay co44and Cor t$e %a4!son :onastery data set%&:%/".[[$E. %a4!son recorded t$e social interactions a4ong agro! oC 4onks and collected n4eros socio4etric rankings.Dring $is stay a crisis in t$e cloister de)elo!ed t$at

reslted in t$e e@!lsion oC Cor 4onks and t$e )olntaryde!artre oC se)eral ot$ers. 2n t$e end, only Cor re4ained int$e 4onastery -ona)entre, -ert$old, &4brose and oisE.=3+ersion 1.0S72"(T]Data>Dis!layData>%!reads$eets >:atri@>ile> /!en


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%a4!son coded Cor ty!es oC relations, #it$ se!arate 4atricesindicating !ositi)e and negati)e ties. (ac$ 4onk ranked only $isto! t$ree c$oices on t$at tie. T$e relations are estee4 %&:(%Eand disestee4 %&:D(%E, liking %&:V N t$ree diCCerent ti4e!eriods #ere recordedE and disliking %&:DV N only one ti4e

!eriodE, !ositi)e inClence %&:2"E and negati)e inClence%&:"2"E, !raise %&:BE and bla4e %&:"BE. 2n eac$ 4atri@ 5indicates t$e $ig$est or Cirst c$oice and 1 t$e last c$oice.%o4e sb8ects oCCered tied ranks Cor t$eir to! Cor c$oicesE.Dis!lay t$e Cile yorselC in order to see t$e co4!lete ot!t.1;"e@t, sing 72"(TAs s!reads$eet Cnction, o!en t$e Cile as as!reads$eet and note t$at eac$ 4atri@ is stored on a se!arates$eet.

igre 9.19 72"(T /t!t og dis!laying %a4!sonAs :onasteryData"etDra#

-eCore looking at t$e )ariety oC tools 72"(T $as Coranalyzing 4lti!le@ data, letAs Cirst )isalize t$e %a4!son datasing "etDra#. &s #e sa# in $a!ter 5, "etDra# allo#s sers to

se 4lti!le lines #it$ diCCerent colors or stylesE and o)erlayone relation on to! oC anot$er iC t$e data are stacked as4lti!le 4atrices #it$in t$e sa4e Cile e.g., like t$e %a4!sondataE. /!en t$e H%&:%/".[[$I1;T$e %a4!son data is one oC t$e standard datasets t$at co4es#it$ 72"(T, so yo can Cind it in t$e 72"(T data Ciles Colder.&lso, nder 72"(TAs el! Cnction sa4!le datasetsE, yo canCind a 4ore co4!lete descri!tion oC t$e %a4!son data.


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=5+ersion 1.0S"etDra#] ile>/!en >7cinet dataset>"et#orkro!erties>ines>olor>Belation

S72"(T]Data>7n!ackdataset, sing t$e ile>/!en> 7cinet dataset>"et#ork co44and.Becall t$at t$e HBelsI tab see igre 9.1 belo#E allo#s yo toselect #$ic$ net#ork to )ie#, #$ic$ can be seCl Cor co4biningand s#itc$ing back and Cort$ bet#een relations.

Wo can also assign diCCerent colors to t$e )arios relationsby sing t$e dialog bo@ not s$o#nE t$at t$ero!erties>ines>olor>Belation co44and calls !. T$ere are ot$er#ays to color relations in "etDra#, bt t$is see4s to be t$e 4oststable a!!roac$ at least Cor no#E.72"(T

"e@t, let s e@a4ine at $o# to n!ack stacked net#ork data in72"(T. To do t$is in 72"(T si4!ly c$oose t$e Data>7n!ackco44and. T$is brings ! an H7n!ackI dialog bo@ igre 9.1


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=9+ersion 1.0Data>Ooin

igre 9.1Ooin co44and. T$is brings ! a HOoinI dialog bo@ igre9.1=, ne@t !ageE. ere, 2A)e c$osen to re8oin estee4 %&:(%E,liking %&:V5E, !ositi)e inClence %&:2"E and !raise %&:BEinto a single Cile called HOoined.I

igre 9.1= 72"(T OoinK:erge Dataset Dialog -o@"ote t$at in t$e abo)e e@a4!le #e c$ose H:atricesI nder t$e

HDi4ensions to 8oinI o!tions on t$e !!er leCt $and side oC t$e

dialog bo@. &s t$is Cigre sggests, yo can also co4bine t$ero#s oC t#o or 4ore 4atrices kee!ing t$e col4ns t$e sa4eE ort$e col4ns oC t#o or 4ore 4atrices kee!ing t$e ro#s t$e sa4eE.T$is co44and can be Gite seCl Cor co4bining and analyzing t#oN4ode i.e., aCCiliationE 4atrices.=+ersion 1.0TransCor4 >:atri@ /!erations > Fit$in dataset >&ggregations


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Data>Dis!layTransCor4 >:atri@ /!erations >-et#een datasets >%tatistical%44aries

Wo 4ay #ant to create a singleN)aled 4atri@ Cro4 a series oCstacked 4atrices like t$e %a4!son data #e 8st 8oinedE. To do

t$is #e need to se t$e TransCor4>:atri@ /!erations>Fit$indataset>&ggregations co44and, #$ic$ brings ! t$e Collo#ingdialog bo@ igre 9.1E.

igre 9.1 72"(T Fit$in Dataset &ggregations dialog bo@&Cter issing t$is co44and, se t$e Data>Dis!lay co44and to see#$et$er t$is #orked as e@!ected.

igre 9.1; 72"(T -et#een Dataset %tatistical %44aries Dialog-o@

"e@t, let s ass4e t$at #e $a)e not yet co4bined )arios4atrices into a single, stacked dataset, bt yo still #ant toco4bine i.e., s4E t#o or 4ore 4atrices into a singleN)aled4atri@. 72"(T allo#s yo to do t$is as #ell alt$og$ it doesnot al#ays #ork nCortnatelyE sing t$e TransCor4>:atri@/!erations>-et#een datasets>%tatistical %44aries co44and, #$ic$brings ! a dialog bo@ igre 9.1;, !re)ios !ageE. lick /V and


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72"(T co4bines t$e 4atrices into a singleN4atri@ and dis!lays asingleN)aled 4atri@ in an ot!t log.=

igre 9.35 72"(T /t!t og oC &ggregated :atri@=;+ersion 1.0TransCor4 >:atri@ /!erations >-et#een datasets >%tatistical%44aries

Wo can also se t$e Data>Dis!lay co44and to e@a4ine t$eaggregated 4atri@. 2C all #e #anted #as an aggregated 4atri@, #edid not $a)e to Cirst stack t$e ten 4atrices. 2nstead, #e cold$a)e aggregated t$e data sing 72"(TAs TransCor4>:atri@/!erations>-et#een datasets>%tatistical %44aries co44and nots$o#n N see igre 9.1; abo)eE. T$e ad)antage oC stacking t$e4atrices is t$at it allo#s s to se so4e oC "etDra#As 4ore$el!Cl Ceatres e.g., assigning diCCerent colors to linesindicating diCCerent ty!es oC ties N see igre 9.33 abo)eE.

ST*8 :atri@ /!erations -et#een Datasets2n!t Datasetsear-ro#se'JDoc4ents+Doc4ents'.Doc4ents'.Doc4ents'.Doc4ents+Doc4ents'N.Doc4ents

and %ettings:-ean:)2y and %ettings\%ean\:y and %ettings\%ean\:yand %ettings\%ean\:8r' and 5ettings\%ean\:8r' and%ettings:-ean:)2y and %ettings:-ean:)2yD oc4ents\% ociology+" % \: anal\7 l " ( T D oc4ents\%ociology%" % \: anal:O l " ( T D oc4ents\% ociology+" % \:anal:O l " ( T D oc4ents\% ociology+" % \: anal:O l " ( T Doc4ents\% ociology+" % \: anal:O l " ( T D oc4ents\%


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ociology+" % \: anal:O l " ( T D oc4ents\% ociology+" % \:anal:O l " ( TData\-siness P inance T Data:Rogistical lace Ties.[Data:D!erational Ties.tttt$ Data:Drganizational Ties.tt[Data\Beligios Ties.tttt$ Data\%c$ool Ties.tttt$ Data\T raining

Ties.tt$/t!t Dataset"oordin bdaN%4Rl/!tions2N7se boolean 4at$2N2gnore diagonalin sGare 4atricesF Data 4ay contain4issing )ales

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igre 9.39 72"(T -et#een Dataset %tatistical %44aries Dialog-o@&ggregating and :ani!lating "oordinAs "et#orks & :ore o4!le@(@a4!le

/C corse, 8st becase t#o !eo!le are 4e4bers oC t$e sa4eorganization or attend t$e sa4e e)ent does not 4ean t$at t$eynecessarily are Criends or e)en kno# one anot$er. T$s, #e 4ay#ant to se so4e sort oC H4e4bers$i!I t$res$old beCore concldingt$at a tie actally e@ists bet#een t#o actors. ooking at t$e"oordin data, let s ass4e Cor illstrati)e !r!oses t$at a tiee@ists bet#een t#o actors iC t$ey are Criends, kin or co44nicate#it$ one anot$er or t$ey are 4e4bers oC or !artici!ated in t#o or4ore oC t$e sa4e gro!s or e)ents. 2n ot$er #ords, iC t#o !eo!le

only attended t$e sa4e sc$ool, t$en #e #ill not ass4e t$at a tiee@ists bet#een t$e4. o#e)er, iC t$ey attended t$e sa4e sc$ooland are 4e4bers oC t$e sa4e 4osGe or !artici!ated in t$e sa4eo!eration, are 4e4bers0+ersion 1.0TransCor4>Dic$oto4izeoC t$e sa4e organization, etc.E t$en #e #ill ass4e t$at a tiedoes e@ist bet#een t$e4. o# can #e ca!tre t$is ass4!tion singsocial net#ork analysis? Fe #ill Cirst only aggregate "oordinAsaCCiliation net#orks sing 72"(TAs TransCor4>:atri@

/!erations>-et#een datasets>%tatistical %44aries co44and igre9.39, !re)ios !ageE.

"e@t, #e se 72"(TAs TransCor4>Dic$oto4ize co44and igre9.3E to assign a H1I Cor e)ery !air oC actors t$at s$ares t#o or4ore 4e4bers$i!s and a H/I Cor e)ery !air oC actors t$at s$aresone or Ce#er 4e4bers$i!s. T$is creates a ne# 4atri@ oC H0AsI andH1AsI igre 9.3


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igre 9.3 72"(T Dic$oto4ize -inarizeE Dialog -o@iCC8 /t!t og [9D2/T/:2M( :&TB2X((2n!t dataset Dic$oto4ization rle Diagonal )alid? /t!tdataset &bdl :alik &bdl BaC &bdl Bo$i4 &bdlla$ %nata &bdlla$%ngkar &b -akar -a'asyir &b D8ana$ &b ida &ceng Vrnia&c$4ad asan &dng &gs &$4ad &$4ad BoCiG Bid$o &$4ad %ayid:alana &8engan :asdki &kra4 &li 6$Cron &niC %olc$andin &!y&ris :nandar &se! Oa8a &s4ar atin %ani &z$ari sin -a$ardin%ole$ $andra\Doc4ents+i.8E 1 iCW(%

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+ersion 1.0Fe can no# stack #it$ t$e Criends$i!, kins$i! and internal

co44nication net#orks by sing 72"(TAs Data>Ooin co44and nots$o#nE, #$ic$ reslts in t$e net#ork 4a! created by "etDra#Es$o#n in igre 9.3=. &s yo can see t$is net#ork is not nearly

as dense as t$e one s$o#n in igre 9.33, #$ic$ 4akes sense since#e eCCecti)ely treated all aCCiliation ties bet#een actors asonly one tie, and t$at #as only t$e case iC t$ey s$ared t#o or4ore aCCiliations. /b)iosly, #e cold $a)e sed diCCerentass4!tions in creating t$is 4odiCied 4a! oC "oordinAs net#ork,bt t$at is beside t$e !oint $ere. &ll #e are interested ins$o#ing at t$is 8nctre is $o# #e can 4ani!late )ariosnet#orks in diCCerent #ays to reClect diCCerent ass4!tions.

igre 9.3= "et#ork :a! oC "oordinAs &ggregated "et#ork:lti!le Belations in a8ek

Fit$ )ersion 1.03 a8ek added a Ceatre t$at allo#s sers to#ork #it$ 4lti!le@ data. o# does a8ek store 4ltirelationalnet#ork data? 2t does so by allo#ing s to assign relationn4bers to a set oC ties i.e., arcs, edgesE. igre

9.3 adgett 4arriage and bsiness net#orksE illstrates $o#sc$ data are recorded and stored. &s yo can see t$at relationn4bers and na4es are added to t$e edges or arcsE state4entsaCter t$e list oC )ertices i.e., nodesE.3+ersion 1.0Sa8ek N Dra# %creen] /!tions>olors>(dges >Belation "4ber/!tions>olors>&rcs >Belation "4ber


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/!tions>olors >Belation olors/!tions>ines>Dra# in es >Belations adgett.net N"ote!ad2

ile

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5 ; 19 = 19 11 19 1 1 11 1

1 1= 1= 1< 1; 15 1; 19 1; 1< 11019 1111 1151 1151< 1l*(dges 3-siness5 15 < 15 ; 1 +

> 1igre 9.3 adgett :arriage and -siness "et#ork Data in a8ekor4at

&s #it$ "etDra# #e can re!resent t$e relation n4ber oC a lineby line color, #$ic$ can be done in t$e Dra# screen #it$ t$e/!tions>olors> (dges>Belation "4ber Cor edgesE and/!tions>olors>&rcs>Belation "4ber Cor arcsE co44ands. Fe canc$oose t$e color oC eac$ relation n4ber in t$e /!tions>

olors>Belation olors dialog screen. Fe can also dra# t$e linesoC 8st one relation by selecting a !articlar relation n4ber int$e /!tions>ines> Dra# ines>Belations dialog bo@. igre 9.3;ne@t !ageE !resents a net#ork 4a! oC t$e adgett data #$ere4arriage ties are colored red and t$e bsiness ties are coloredble. F$en t#o actors s$are a tie e.g., -isc$eri and erzziE,a8ek colors t$e ties by t$e last relation in t$e Cile in t$iscase, bsiness bleE. Becall t$at "etDra# colors 4lti!lerelations grey.5+ersion 1.0

S:ain %creen] "et>TransCor4 >:lti!le Belations >(@tractBelations"et>TransCor4 >:lti!le Belations >$ange Belation "4berS72"(T]Data>(@!ort>DSa8ek]ile>"et#ork>%a)e


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F&MM2igre 9.3; "et#ork :a! oC adgett :ltirelational Data

a8ek allo#s s to e@tract one or 4ore relations Cro4 a4lti!le relations net#ork #it$ t$e "et>TransCor4>:lti!leBelations>(@tract BelationsE co44and. F$en #e isse t$is co44anda8ek generates a ne# net#ork Cor eac$ oC t$e selected relationn4bers, !reser)ing t$e relation n4ber. Fe can also recoderelation n4ber and c$ange relation labels #it$ t$e"et>TransCor4> :lti!le Belations>$ange Belation "4berNabelco44and. Fe can also c$ange t$e label na4e oC a relation by

o!ening and editing t$e a8ek Cile in a te@t editor sc$ as"ote!ad. T$at is $o# t$e labels #ere added to igre 9.3 abo)e."oordinAs "et#orks in a8ek

To get at sense oC $o# to #ork #it$ sc$ data in a8ek, #e#ill e@!ort t$e "oordin o4bined "et#ork #e aggregated in 72"(Tto a8ek sing 72"(TAs Data>(@!ort>D co44andL t$is brings !t$e Collo#ing dialog bo@ igre 9.50, ne@t !ageE, #$ic$ by no#s$old be Ca4iliar to yo. &s beCore, yo #ill #ant to c$ange t$eot!t dataset e@tension Cro4 H.t@tI to H.dat.I &Cter reading t$eH.datI Cile in "oordin, sa)e it as a H.netI Cile, sing a8ekAsile>"et#ork>%a)e co44and.

9+ersion 1.0(@!ort as D Cile2n!t dataset /t!t Cor4at Diagonal !resent Sedgelist onlyETy!e:ini44 tie )al allo#ed Deci4al !laces ield #idt$ 6arantees!ace age #idt$ (4bed ro# labels (4bed col4n labels (4bed4atri@ labels /t!t dataset


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11' &dng 0.533(@!ort>a8ek>"et#orkSa8ek]"et#ork>Bead"ets>7nion oC ine Dra#>Dra#"et>TransCor4>Be4o)e >:lti!le lines>%4 +ales

&ggregating Data in a8ekF$ile #e can aggregate data Ciles in a8ek, nCortnately, #ecan only co4bine t#o Ciles at a ti4e, #$ic$ is #$y yo #ill!robably do 4ost oC yor Cile aggregation in 72"(T. T$at said,#e brieCly illstrate $o# to aggregate Ciles in a8ek. Fe #illCirst need to e@!ort t#o oC t$e "oordin Ciles sing 72"(TAsData>(@!ort>a8ek>"et#ork co44and not s$o#nE. "e@t, o!en a8ekand read t$e t#o Ciles into 4e4ory sing a8ekAs "et#ork>Beadco44and. Be4e4ber to look Cor Ciles #it$ a .net e@tension becaseyo e@!orted t$e data Cro4 72"(T sing t$e (@!ort>a8ek o!tion.To co4bine 4atrices in a8ek, yo need to Cirst identiCy t$e t#o4atrices yo intend to co4bine. 2n a8ek $ig$lig$t t$e Cirst4atri@ in t$e Cirst net#ork dro! list and t$e second in t$esecond net#ork dro! list see igre 9.59E. T$en, select t$e"ets>7nion oC ines co44and. T$is #ill create a ne# net#ork t$ata8ek labels sion oC 1 and3, #$ic$ yo can )isalize t$eco4bined net#ork sing t$e Dra#>Dra# co44and.a8ek (-(


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ile "et "ets /!erations artition artitions +ector+ectors er4tation er4tations lster ierarc$y/!tions Dra# :acro 2nCo Tools"et#orks

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igre 9.59 T#o "et#orks ig$lig$ted in a8ekAs "et#ork Dro!do#n

istsF$en a8ek co4bines net#orks sing t$e 7nion oC ines co44and, ittreats t$e4 as a single relation #it$ 4lti!le lines. 2C yo #antto co4bine t$e t#o net#orks into a single )aled net#ork, 4akesre t$at t$e ne#ly created i.e., CsedE net#ork is $ig$lig$tedin t$e Cirst net#ork dro! list, t$en select t$e %4 +alesco44and nder t$e "et>TransCor4>Be4o)e>:lti!le lines sb4en.ositi)e and "egati)e Belations in 72"(T and a8ek

2n t$is section #e #ill try so4et$ing a bit diCCerent. &s yokno#, t$e %a4!son data contains bot$ !ositi)e e.g., likeE andnegati)e dislikeE socio4etric data. Fe are going to 4lti!ly one

oC t$e negati)e net#orks HdislikeIE by HN1I in order totransCor4 t$e )ales into Hnegati)eI )ales and t$en add t$isne#ly created 4atri@ to one oC t$e !ositi)e net#orks HlikeI atti4e 5E. T$is co4bined=+ersion 1.0S72"(T]Data>Dis!lay


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TransCor4 >:atri@ /!erations > Fit$in dataset >ell#iseTransCor4ationsTransCor4 >:atri@ /!erations >-et#een datasets >%tatistical%44ariesnet#ork #ill contain bot$ !ositi)e and negati)e )ales in t$e

)arios cells. Fe #ill t$en e@!ort t$is net#ork to a8ek and)isalize it.irst, conCir4 t$at t$e negati)e disliking relation

%&:DV.[[$E is indeed coded #it$ !ositi)e n4bers by dis!layingt$is Cile in 72"(T sing t$e Data>Dis!lay co44and or t$edis!lay icon bttonE. "e@t, #e #ill transCor4 t$ese !ositi)e)ales into negati)e ones sing t$e TransCor4>:atri@ /!erations>Fit$in dataset>ell#ise TransCor4ations co44and. T$is brings !t$e Collo#ing dialog bo@ igre 9.5E. "ote t$at #e $a)eselected H%&:DV.[[$I as or in!t dataset and H%&:DV3.[[$I ast$e na4e oC t$e transCor4ed ot!tE dataset. Fe $a)e alsoc$ecked t$e H"egati)eI bo@ a4ong t$e TransCor4ation o!tions.lick H/VI and yo s$old get an ot!t log t$at indicates t$att$e )ales in t$e ne# 4atri@ are negati)e.

igre 9.5 72"(T Fit$in Dataset ell#ise TransCor4ationsDialog -o@

T$e ne@t ste! is to add t$is ne#ly created 4atri@ to t$e%&:V5.[[$ 4atri@. To do t$is, #e #ill once again se 72"(TAsTransCor4>:atri@ /!erations>-et#een datasets>%tatistical

%44aries co44and see igre 9.5


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n!t Dataseis lear-ro#se

&rogra4 iles FialyticTec$nologies+7cinetBead


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Dra#>Dra#ayot>(nergy>Va4adaNVa#ai>ree/!tions>%ize >oC +erticesData>(@!ort>a8ek>"et#ork co44and is becase at least crrentlyE

#$en yo se t$e latter co44and, 72"(T e@!orts t$e negati)e cell)ales as !ositi)es.a8ek

/!en a8ek and read in t$e net#ork data yo 8st e@!orted Cro472"(T sing t$e ile>"et#ork>Bead co44and. Be4e4ber t$at t$enet#ork Cile yo are trying to read $as a .dat e@tension not a.net. one.E "e@t, )isalize t$e net#ork sing t$e Dra#>Dra#co44and and energize it sing one oC a8ekAs 4a!!ing algorit$4seit$er Va4adaNVa#ai or rc$ter4an Beingold or bot$E. "ote t$att$ere are bot$ solid lines and negati)e lines bet#een t$e nodes.2n a8ek solid lines indicate !ositi)e connections #$ile dottedlines indicate negati)e connections.

2C t$e nodes are $ard to distingis$ #it$ all oC t$e lines,yo can increase t$e size oC t$e node sing t$e /!tions>%ize>oC+ertices co44and in a8ekAs Dra# screen. igre 9.5 ses a)erte@ size oC 10. 6enerally, $o#e)er, it is #ise to se t$edeCalt setting H0IE, #$ic$ tells a8ek to ato4atically set t$esize oC t$e )ertices. T$is is an es!ecially seCl o!tion #$ennode size reClects an attribte t$at )aries considerably e.g.,age, centrality, etc.E.


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igre 9.5 a8ek Dra#ing oC %a4!son :onastery iking andDisliking Data;0 +ersion1.09.= %44ary and onclsion

T$is c$a!ter $as Cocsed on 4et$ods Cor collecting and

recording social net#ork data. 2t began #it$ a brieC discssionon $o# social net#ork analysts deCine t$e bondaries oC t$enet#orks t$ey are e@a4ining. 2t t$en 4o)ed to a brieC discssionoC t$e diCCerence bet#een ego and co4!lete net#orks, noting t$atsocial net#ork analysts generally se co4!lete net#orks #$ena!!lying social net#ork 4et$ods. 2ndeed, 4ost social net#ork4et$ods ass4e t$at one is #orking #it$ co4!lete social net#orkdata. "e@t, #e considered t$e diCCerent ty!es oC data socialnet#ork analysts se oneN4ode net#ork data, t#oN4ode net#orkdata and attribte data. Fe t$en discssed t$e )arios #ays t$atsocial net#ork analysts collect net#ork data beCore looking at$o# social net#ork data are recorded in 4atri@ Cor4. T$e Cinalsection oC t$is c$a!ter t$en looked at )arios #ays oCaggregating 4lti!le net#orks into bot$ HstackedI and single)ale4atrices. 2t is no# ti4e to trn or attention to t$e )ariosCa4ilies oC 4etrics t$at analysts se to e@a4ine social net#orks.;1+ersion 1.0$a!ter "(TF/BVT//6B&W

"et#orks can diCCer considerably Cro4 one anot$er, and t$ereis considerable e)idence t$at sggests t$at a net#orkAsto!ogra!$y i.e., its o)erall strctreE $as an eCCect on its

!erCor4ance andKor eCCiciency. or instance, social 4o)e4entt$eorists $a)e Cond t$at t#o 4easres oC a net#orkAs o)erallc$aracteristics N net#ork density and net#ork centralization Ni4!act a social 4o)e4entAs eCCecti)eness Diani 3003L /sa 3005E,and &4i eda$zr and &rie erliger 300


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net#ork to!ogra!$y, #e begin by brieCly retrning to6rano)etterAs discssion oC #eak and strong ties..1 Feak Ties and %trong Ties Bed@

(arlier #e sa# $o# :ark 6rano)etterAs 1;=5L 1;=9E disco)eredt$at #$en it ca4e to Cinding 8obs, !eo!le #ere Car 4ore likely to

se !ersonal contacts t$an ot$er 4eans. :oreo)er, oC t$ose #$oCond t$eir 8obs t$rog$ !ersonal contacts, 4ost oC t$e !ersonalcontacts #ere #eak ties i.e., acGaintancesE rat$er t$an strongties i.e., close CriendsE. T$is #as becase not only do #e tendto $a)e 4ore #eak ties and strong ties becase #eak ties de4andless oC or ti4eE, bt also becase or #eak ties are 4ore likelyto Cor4 t$e crcial bridges t$at tie toget$er densely knitclsters oC !eo!le see igre .1 belo#E. 2n Cact, iC it #erenot Cor t$ese #eak ties, 6rano)etter arges, t$ese clsters #oldnot be connected at all. T$s, #$ate)er is to be s!read e.g.,inCor4ation, inClence, and ot$er ty!es oC resorcesE, it #illreac$ a greater n4ber oC !eo!le #$en it !asses t$rog$ #eak tiesrat$er t$an strong ones. :oreo)er, 6rano)etter arges t$at actors#$ose;3+ersion 1.0#it$ Ce# #eak ties are 4ore likely to HconCined to t$e !ro)incialne#s and )ie#s oC t$eir close CriendsI 6rano)etter 1;=5E.igre .1 %trong and Feak Ties

6rano)etter does not arge t$at strong ties #ere oC no se,$o#e)er. e notes t$at #$ile #eak ties !ro)ide indi)idals #it$access to inCor4ation and resorces beyond t$ose a)ailable int$eir i44ediate social circles, strong ties $a)e greater

4oti)ation to be sorces oC s!!ort in ti4es oC ncertainty./t$ers $a)e noted t$is as #ell. HT$ere is a 4ontain oC researc$s$o#ing t$at !eo!le #it$ strong ties are $a!!ier and e)en$ealt$ier becase in sc$ net#orks 4e4bers !ro)ide one anot$er#it$ strong e4otional and 4aterial s!!ort in ti4es oC grieC ortroble and so4eone #it$ #$o4 to s$are liCeAs 8oys and tri4!$sI%tark 300=5=E.

24!licit in 6rano)etterAs arg4ent is t$at !eo!leAs net#orksdiCCer in t$e n4ber oC #eak and strong ties t$ey $a)e. T$eirnet#orks can range Cro4 local or !ro)incial ones consisting oC!ri4arily oC strong, redndant ties and )ery Ce# #eak ties to

#orldly or cos4o!olitan net#orks consisting oC n4eros #eak tiesand )ery Ce# strong ties %tark 300=5=N5E. :oreo)er $isanalysis i4!licitly sggests t$at t$at ideally !eo!lesA net#orkss$old consist oC a 4i@ oC #eak and strong ties. 2ndeed, as #es$all see belo# %ection .3E escosolido and 6eorgiannaAs stdyoC sicide sggests t$at indi)idals s$old seek to e4bedt$e4sel)es #it$in a net#ork c$aracterized by a 4i@ oC #eak and


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strong ties #eak ties to !ro)ide t$e4 access to t$e Clo# oCinCor4ation and ot$er resorces

;5+ersion 1.0t$rog$ot t$e social strctre and strong ties to !ro)ide t$e4#it$ s!!ort and a strong sense oC belonging, 4eaning andidentity.Feak and %trong Ties in t$e "e# Work &!!arel 2ndstry

&n ideal 4i@ oC #eak and strong ties a!!ears to not only!ro)ide beneCits at t$e indi)idal le)el bt also at t$e

organizational le)el. 2n $is stdy oC t$e "e#Work a!!arel indstry, -rian 7zzi 1;;


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Cir4s t$at are too e4bedded sCCer becase t$ey cease to $a)eaccess to inCor4ation Cro4 distant !arts oC t$e net#ork, #$ic$4akes t$e4 )lnerable to ra!idly c$anging sitations. T$is lead7zzi to arge t$at Cir4s s$old seek to 4aintain a balance oCe4bedded and 4arket ties. 2n s!!ort oC t$is $e Cond t$at t$e

to!ogra!$y oC interCir4 net#orks i.e., in ter4s oC e4bedded and4arket tiesE )aried and t$at a 7Ns$a!ed or cr)ilinearrelations$i! e@ists bet#een t$e degree oC e4beddedness and t$e!robability oC Cir4 Cailre 7zzi 1;;


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i44ediate social gro!. T$s, t$ey oCten lack t$e ties to !eo!lei.e., Criends, Ca4ilyE #$o 4ig$t sto! t$e4 Cro4 taking t$eCinal, Catal ste!. :oreo)er, since it is co44on in $ig$lyNclstered gro!s Cor t$e gro!As o!inion to s$iCt to#ard e@tre4e)ersions oC t$eir co44onlyN$eld belieCs, it is not sr!rising

t$at so4eti4es t$ese gro!s trn to e@tre4e be$a)iors sc$ assicide. T$e Oonesto#n and ea)enAs 6ate 4ass sicides a!!ear tobe an e@a4!le oC t$is."et#ork Density in 72"(T and a8ek

To see $o# to calclate net#ork density in 72"(T and a8ek,#e #ill se t$e H"oordin o4bined "et#orkI Cile, #$ic$ is astacked 4atri@ oC ten 10E diCCerent "oordin oneN4odeE net#orks.2n 72"(T yo calclate net#ork density sing t$e ne#EDensity/)erall co44and Cond nder t$e "et#ork> o$esion>Densitysb4en. -eCore doing t$is, $o#e)er, #e need to Cirst dic$oto4izebinarizeE t$e net#ork becase so4e oC t$e net#orks in t$is Cileare )aled e.g., t#o !eo!le 4ay $a)e t#o or 4ore ties becaset$ey !artici!ated in t#o or 4ore oC t$e sa4e training e)ents orbelong to t#o 4ore oC t$e sa4e organizationsE. To dic$oto4ize anet#ork in 72"(T, select t$e TransCor4> Dic$oto4ize co44and,#$ic$ calls ! a dialog bo@ igre .3 belo#E t$at asks31Drk$ei4 essentially t$at social integration and socialreglation $a)e a cr)ilinear eCCect on sicide. ig$ le)els oCintegration and reglation are !ositi)ely related to t$e siciderate as are lo# le)els oC integration and reglation. -y contrast4oderate le)els oC integration and reglation are negati)elyrelated to t$e sicide rate.33Becall t$at !eo!le #$o li)e in dense net#orks are 4ore likely

to Collo# acce!ted nor4s and be$a)ior.;+ersion 1.0S72"(T] "et#ork>o$esion >Density >ne#E Density /)erallyo to indicate #$ic$ data Cile yo #ant to dic$oto4ize. Tell72"(T to se t$e H"oordin o4bined "et#orkI Cile. "ote also t$at72"(T also !ro)ides a HctoCC o!eratorI and HctNoCC )aleIo!tions t$at allo# yo to tell 72"(T #$at yo #ant yor ctoCC)ale Cor dic$oto4izing t$e net#ork to be. ere, #e $a)e c$osento acce!t 72"(TAs deCalt becase #e #ant e)ery )ale in eac$ oCt$e ten 4atrices t$at is greater t$an zero to be coded to 1. "ot

also t$at $as a deCalt setting Cor t$e ot!t Cile na4e.


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igre .3 72"(TAs Dic$oto4ize Dialog -o@"o#, #e are ready to calclate t$e density oC t$e ten

net#orks. 72"(TAs ne# o)erall density co44and calls ! a dialogbo@ see igre .5 belo#E #$ere yo s$old indicate as yorin!t dataset t$e H"oordin o4bined "et#ork6T/I net#ork i.e.,t$e recently dic$oto4ized net#orkE. lick /V. T$e resltingot!t log #ill gi)e yo density scores Cor eac$ oC t$e net#orksin t$e Cile.

igre .5 72"(TAs Density Dialog -o@;:atri@ /!erations > Fit$in dataset >&ggregationsTransCor4>Dic$oto4ize"et#ork>o$esion >Density >ne#E Density /)erallS72"(T]Data>(@!ort>DSa8ek] "et>TransCor4 >&rcs ^(dges>&ll"et>TransCor4 >Be4o)e oo!s"et>TransCor4 >:lti!le Belations >(@tract Belations2nCo>"et#ork>6eneral

/C corse, #e 4ay also be interested in aggregating t$e tennet#orks into a single net#ork and t$en calclating t$e resltingnet#orkAs density. To do t$is #e se 72"(TAs TransCor4>:atri@/!erations>Fit$in datasets>&ggregations co44and, #$ic$ #ediscssed at lengt$ in $a!ter 9. &Cter aggregating t$e stacked4atri@, #e t$en need to dic$oto4ize t$e net#ork becase no# so4ecells $a)e )ales oC greater t$an oneE sing 72"(TAsTransCor4>Dic$oto4ize co44and. &Cter aggregated 4atri@ is


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dic$oto4ized, t$en #e #old calclate t$e density oC t$e o)erallnet#ork sing t$e "et#ork>o$esion>Density>ne#E Density /)erallco44and.

F$ile calclating density Cor indi)idal net#orks is )erysi4!le in a8ek, it is so4e#$at 4ore co4!licated to calclate

density Cor 4ltirelational net#orks, #$ic$ is #$y #$en #orking#it$ a stacked 4atri@, yo #ill !robably #ant to esti4ate yordensity 4easres in 72"(T. "e)ert$eless, it is $el!Cl to see$o# it is done so yo do not need to s#itc$ back and Cort$bet#een !rogra4s nnecessarily.

-eCore calclating net#ork density in a8ek #e need to Cirste@!ort t$e H"oordin o4bined "et#ork6T/I Cile Cro4 72"(T toa8ek

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