Unevenness in Network Properties on the Social Semantic Web

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UNEVENNESSIN NETWORK PROPERTIES ON THE SOCIALSEMANTICWEB

RAF GUNS

∗

Abstrat. Thispaper studies unevennessinnetworkpropertiesonthe soialSemantiWeb. First,weproposea two-step

methodologyfor proessing and analyzing soialnetwork data fromthe Semanti Web. Usingthe SPARQLquerylanguage, a

derivedRDFgraphanbeonstrutedthatistailoredtoaspeiquestion. Afterabriefintrodutiontothenotionofunevenness,

thismethodologyisappliedtoexamineunevennessinnetworkpropertiesofsemantidata. ComparingLorenzurvesfordierent

entralitymeasures,itisshownhowexaminationsofunevennessanprovideruialhintsregardingthetopologyof(soial)Semanti

Webdata.

Keywords: semantiWeb,soialnetworkanalysis,SPARQL,unevenness

1. Introdution. The soial Semanti Web is abroad,non-tehnial term, referringto data onthe

Se-manti Web (enoded in RDF) that ontain soial information. The most prevalent ontology on the soial

SemantiWebistheFOAF(FriendOfAFriend)voabulary[9℄. FOAFanexpressinformationaboutpeople

and the things they make and do and espeially about how they are related. In this artile, we will use a

soio-ulturalontologythatis(partly)basedonFOAFandalsousesoneptsfromotherwell-knownontologies

likeDublin Core.

TheSemantiWeb[5℄in generalis oneivedasalarge-saledistributedinformationsystem. Whilesome

onstituentsarestillindevelopmentanditsurrentuptakeisrelativelymodest,theSemantiWebgraphalready

showsthetraitsofaomplexsystem. Complexsystemsareenounteredinmanydierentontextsandinlude

suhdiverseexamplesas omputernetworks,soialnetworks,neuralnetworksandellularnetworks[13℄. Asa

omplexsystem,theSemantiWebisharaterizedby[3,17℄:

•

Small world properties: Made famous by Stanley Milgram's [25℄ letter experiment, the small world

notionrefers to the fat that the average shortestpath lengthin a graphis very short (omparable

tothat of arandomgraph). In pratie,thismeans thatit takesonly afewstepsto reah any other

(reahable)node in the network. It is advisable to also takethelongest shortestpath, known asthe

diameter,into aount. Duringthelast deade,severalmodelshavebeenproposed toaountforthe

small-worldeet[26, 31℄.

•

Highlustering: Theneighboursofagivennodearelikelyalsoneighboursofeahother.

•

Skewed degree distribution: The probability

P

(

k

)

that a node has degree

k

(is onneted to

k

other

nodes)isnotrandomlydistributed. Instead,itfollowsapowerlaw

P

(

k

)

≈

Ak

−

γ

. Moreover,omplex

systemstypiallyexhibitpowerlawdistributions inmorethanone way. With regardtotheSemanti

Web,previousresearhhasshownthatadiversityof relationssuhastherelationbetweenwebsites

(domain names) and their numberof Semanti Web douments orthe relation between an ontology

anditsfrequenyofusefollowsapowerlaw[15℄.

Theseproperties,however,raiseseveralquestionsaswell. Inthisartile,werstdisussatwo-step

method-ologyfor extratingthe SemantiWeb data (or `semanti data' forshort) that weare interested in from the

rest. Wethenfousonthelast harateristiandtrytoomparetheskewednessofseveralnetworkmeasures.

Wetrytoprovideananswertothefollowingtworesearhquestions.

First,howan dataon thesoial Semanti Webbe used forSoial Network Analysis (SNA)? Signiant

researhinthisareahasalreadybeenperformedby,amongothers,Dingetal.[15℄andPeterMika[23,24℄. Muh

workhasonentratedonaquiringandaggregatingdata(oftenFOAFdata),espeiallymerginginformation

aboutuniquepersonsturns outto befar fromtrivial. Inthe presentartile,weassumethat `lean'semanti

dataarealready availableand onentrateonthefollowingstep: thedevelopmentofamethodologyfor using

one singleRDF graphas the `master', whih an be used asthe basis for several kinds of SNA. Ideally, we

wanttokeepasmuhinformationaspossibleandextratamultitude ofpotentiallyinterestingrelations. This

partiularaspethasreeivedlessattentionsofar.

Seond,itisveryrarelyexaminedhowskewedadistribution is. Howanthisnotionbemeasured?

Quan-tiationofunevennessisruialforathoroughunderstandingofapowerlawdistribution;moreover,itanbe

usedforomparisonpurposesbetweendistributionsandbetweennetworks.

∗

UniversityofAntwerp,InformatieenBibliotheekwetenshap,CST,Venusstraat35,2000Antwerpen,Belgium,

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Both questions will be disussed and demonstrated using semanti data from Agrippa. Agrippa is the

atalogueanddatabaseof theArhiveandMuseumof FlemishCulturalLife(AMVCLetterenhuis,loatedin

Antwerp,Belgium). Whereappliable,theRDFversionbuildsuponexistingontologieslikeFOAFandDublin

Core. Agrippaontainsawealthofinformationaboutboththearhivedmaterialsandthesoio-ulturalators

(peopleandorganizations)thathavereatedthem. WewillmostlyuseAgrippainformationaboutthe237,062

letterspresentattheAMVCLetterenhuis andtheirwritersandreipients.

2. Two-stepmethodology. Semantidataanbestoredinmanydierentways:asa(setof)doument(s)

in one of themany RDF syntaxes [4℄; in a `lassi' relationaldatabase; orin atriplestore, adediated RDF

database. For performane andonveniene reasons,weareusing atriplestore, but mosttehniquesanalso

be performed on, for instane, RDF douments. The triplestore used is Sesame, freely available at http:

//www.openrdf.org/. 1

Partlydue to theirdistributed nature, semantidata may appear quitedazzling: manydierentkindsof

data,drawnfromseveralontologies,betweenwhihamultitudeofrelationsexist. Howanonemakeheadsor

tailsoutofthem? Assumingtheexisteneofasetoffairlylearlydenedquestionstobeanswered,wepropose

atwo-stepmethodology,whihritiallydependsontheSPARQLquerylanguage[27℄oraquerylanguagewith

similarapabilities. Inshort,thetwostepsare:

1. ConstrutanextrationqueryinSPARQLandapplyittotheRDFgraph. Thisyieldsaderivedgraph,

speiallytailoredtothequestion(s).

2. Convertthederivedgraphto aformatintendedforSNA.

Wewillnowdisussbothstepsingreaterdetail,usingapartofAgrippaasanexample(showninFigure2.1).

Both Organization and Person are akind of Agent. A LetterContext tiestogether the dierent partiipants

in theat ofletter-writing: thewriter(s),the reipient(s) andthe letterasaphysial objet. A letter anbe

writtenandreeivedbyeitheranAgentoranAliationContext. Thisreferstoaperson(the`aliatee')ating

onbehalf ofhis/heraliationtoanorganization(the `aliator').

Fig.2.1. Partof theAgrippa ontology,showingtherelationsbetweensixlasses

2.1. SPARQL informationextration. FourSPARQLquerytypesexist: SELECT,CONSTRUCT,ASKand

DESCRIBE.SPARQLqueriesareusuallySELECTqueries,whihreturnatableofresults. Inthisstep,weemploy

CONSTRUCTqueries,whih returnanewRDF graph. A similararhitetureanalso befoundin the MESUR

projet[8,28℄. Wewillrefertotheoriginalgraphassouregraph andtothenewlyonstrutedgraphasderived

graph.

First,we omparetheoriginalgraphin thetriplestoreandthe questionsto beanswered. Some questions

simplyinvolvetheextrationofpartsoftheRDFgraph(ignoringtherest),likethefollowingexample. Suppose

we want to examine only those letters that were reated in an organizational ontext. This boils down to

extratingthelettersthatarewrittenbyanOrganizationoranAliationContext:

PREFIX : <http://anet.ua.a.be/agrippa#>

CONSTRUCT {

?ontext a :LetterContext ;

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:hasLetterWriter ?writer ;

:hasReipient ?reipient ;

:hasLetter ?letter .

}

WHERE {

?ontext a :LetterContext ;

:hasLetterWriter ?writer ;

:hasReipient ?reipient ;

:hasLetter ?letter .

{ ?writer a :Organization } UNION

{ ?writer a :AffiliationContext }

}

Other questions also require knowledge on how relations in the model interat,these involve both

ex-trationand ombination of parts of the model. Here are twoexamples from Agrippa. The following query

onstrutsaderivedgraphofpersonsandtheiraliationstoorganizations. Theresultisabipartitegraph,i.e.

agraphwithtwokindsofnodes(personsandorganizations).

CONSTRUCT { ?person :affiliatedWith ?org }

WHERE {

?aff :hasAffiliator ?org ;

:hasAffiliatee ?person .

}

And the following queryonstruts a simple derived graph that links author(s) and reipient(s) of eah

letter:

CONSTRUCT { ?sender <urn:agrext#writesLetterTo> ?reipient }

WHERE {

?ontext :hasLetterWriter ?sender ;

:hasReipient ?reipient .

}

It should be noted that it is often easier to obtain the desired results using one or more intermediate

extrationqueries. Assuh,aderivedgraphmaybeomethesouregraphinanextstepandsoon. Oneould,

for example, use the result of the rst example asthe soure graphfor the third example query. Although

extrationqueriesareobviouslynotaspowerfulasadediatedprogramorfull-edgedreasoner,theyareoften

suientandmuhfaster toimplement.

Oneoftheadvantages ofstoragein atriplestoreisavailabilityoftheSPARQL protool[14℄. As itsname

implies, the SPARQL protool is designed for exhanging SPARQL queries and results between lients and

servers. ItisentirelybasedonWebstandardslikeHTTPandXML.

2.2. Conversionfor SNA analysis. Oneaderivedgraphhasbeenobtained,itanbestudied. There

exist several projets for visualizing and exploring RDF and FOAF data, suh as FOAF Explorer, 2

RDF-Gravity 3

and Visual Browser. 4

These tools, however, generally donot provide SNA measures like entrality

andlustering,althoughFlink[23℄seemsapromisingexeption. Moreover,theygenerallydonotsaletovery

largegraphs. Aslongasthereexist virtuallynoappliationsthatsuessfullybringnetwork analysistoRDF,

itseemsadvisableto onvertthederivedgraphtoamoregenerileformatfornetworkanalysis.

Thus, while not stritly neessary, this step ensures ompatibility with other SNA eorts and permits

tehniques that are diult to perform on plain RDF graphs. We handle these onversions by integrating

withpyNetConv,aPythonlibrarythatanonverttomostommonformats,inludingPajek,NetworkX,and

GML.

2

http://xml.mfd-onsult .dk/ foaf /ex plor er/

3

http://semweb.salzburgr esea rh .at/ app s/rd f-g ravi ty/

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3. Unevenness.

3.1. The Lorenz urve and the Gini evenness index. The distribution ofdegrees ontheSemanti

Webislikemanyotherrelationshighlyuneven: asmallnumberof nodeshasahugeamountoflinks,while

thevastmajorityhasveryfew. Howan thisunevennessbequantied?

Unevenness or inequality has been studied extensively in eonometris and informetris. Sine not all

existingmeasuressatisfyallneessaryrequirements[1,16℄,wewilllimitthepresentdisussiontotwomethods,

using the following simple array as an example:

X

= (1

,

3 ,

4 ,

7 ,

10 ,

15)

. These numbers ould express the

distributionofwealth,thenumberofpubliationsperauthororthenumberoflinkspernode. Clearly,thereis

someunevenness,buthowmuhexatly?

TheLorenzurve[21℄isagraphialrepresentationofunevenness. First,wedeterminetherelativeamounts:

a

i

=

x

i

P

x

resultingin(1/40,3/40,1/10,7/40,1/4,3/8). ThehorizontalaxisoftheLorenzurvehasthepoints

i/N

(

i

=

1 ,

2 , . . ., N

)

. Thevertialaxisof theLorenz urve hastheirumulativefration:

a

1

+

a

2

+

. . .

+

a

i

. Wethus

onstrut theLorenz urve(Figure 3.1). Thediagonal line representsthe aseof perfet evennesseveryone

possessesthe sameamount. Thefurther theurveisremovedfrom the diagonal,the greatertheunevenness.

Note that we haverankedournumbersin inreasingorder,resulting in aonvexLorenz urve. The onave

Lorenzurveresultsfromrankingindereasingorderandisompletelyequivalent. Completeunevennessone

personhaseverything,andtherestnothingwouldberepresentedasaonvexurvefollowingthebottomand

therightsideoftheplot.

Fig.3.1.ConvexLorenzurveofthearray(1,3,4,7,10,15)

Suppose we want toexpress this unevennessin anumber. A good measureis theGini evennessindex

G

′

[29℄,originallydevisedtoharaterizethedistributionofwealthoversoiallasses[18℄,

G

′

₍

_X

_{) =}

2 µN

2





N

X

j

=1

(

N

+ 1

−

j

)

x

j





−

1 N

with

x

j

ranked in inreasing order and

µ

the meanof the set

x

j

. There exists adiret relationbetweenthe

LorenzurveandtheGinievennessindex:

G

′

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Lorenzurvesdetermineapartialorder: insome,but notall, ases,anorderanbedeterminedfrom the

omparison of twoLorenz urves. Indeed, if oneonvex Lorenz urve is ompletely below another, then the

formerexpresseslessevennessthanthelatter. It shouldbestressedthat Lorenzurvesmay`overlap'orross

eahother. Intheseases,noorderanbedeterminedfrom theurves[29℄.

3.2. Appliation to Agrippa.

3.2.1. Overview of network measures. Letustaketheauthor-reipientgraphonstrutedinthelast

exampleof2.1

N

= 40

,

914

asanexample. Eah nodeisonnetedby5.08linksonaverage,buttheatual

in-andout-degreefollowapowerlawdistribution(Figure3.2). Wewill onsiderthefollowingnetworkmeasures,

mostofwhiharedened byWasserman&Faust[30℄:

•

Degreeentrality(DC):isthenumberoflinks onnetedto agivennode.

•

Betweenness entrality (BTC): haraterizes the importane of a given node for establishing short

pathwaysbetweenothernodes.

•

Closeness entrality(CC):haraterizeshowfastothernodesanbereahedfromagivennode.

•

Pagerank(PR):haraterizestheimportaneofagivennodebyombiningitsnumberofin-linkswith

theimportaneofthenodesthatlinktoit. Thealgorithmwasoriginallyreatedfordeterminingaweb

page'simportane[10℄but hassinebeenusedin manyother ontextsaswell(e.g., [12,22℄).

Thissmalllistofmeasuresisinnowayintendedtobeexhaustive. Manyothermeasuresexistandeventhe

oneslistedherehaveseveralvarietiesthemselves. Theyhavebeenhosenbeausetheyarebothwell-knownand

generallyusedand aepted. Moreover,theyanbeomputedusingstandardsoftwaretools. Fortheurrent

artile,weusedtheigraph Rpakage,available athttp://neurovs.rmki.kfki.hu/igraph/.

The entrality measures listed aboveall have variants for direted and undireted networks, but wewill

onlyonsiderthediretedvariants. Bothdegreeentralityandlosenessentralityhavedierentalgorithmsfor

in-linksandout-links. Weandistinguishbetweenin-degreeentrality(IDC)andout-degreeentrality(ODC),

andbetweenin-losenessentrality(ICC)andout-losenessentrality(OCC).Thisdistintionisnotusefulfor

betweennessentralityandPageRank.

Fig.3.2. Powerlawdistributionforin-degreeandout-degree

3.2.2. Comparison of unevenness between network measures. The graphis not fully onneted,

but themain omponent(

N

= 40

,

303

)aountsfor thevast majority ofnodes(98.5%). Heneforth, wewill

onlyonsider thenodes that arepartof themain omponent,sineverysmallomponents(e.g.,

N

= 2

)an

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in the overall network is obviouslymarginal. We thereforeonsider it methodologiallymoreorret to only

onsidernodesthat arepartofthemainomponent.

ComparingIDCto ODC and ICCto OCC (Figure 3.3), wesee that in bothasesthe measure basedon

in-linksismoreuneven. Inspiteofthisdierene,itshouldbenotedthatinbothasestheshapeoftheLorenz

urveofthein-link-basedmeasureissimilarto thatoftheout-link-basedone.

PageRankis, in asense,amorerened versionof in-degree entrality. Whereas thelatteronly onsiders

the loal neighbourhood (i. e. the number of links to a given node), PageRankalso onsiders the status of

thenodesthat are linkingto agivennode by iterativelypassingstatusbetweennodes. Figure 3.4showsthat

PageRankis atually moreeventhan in-degreeentrality. Inother words: someextremevariationsin degree

are `evened out' by looking at a node's status in the entire network rather than just its number of in-links.

Inspetion ofthedata reveals thatthis isalmost exlusivelydue to nodeswithalownumberofin-linksfrom

some veryhigh status nodes. Put another way, dierenes between PageRankand IDC may be due to IDC

either`overrating'or`underrating'somenodes;atleastforthisexample,thelatterismostlythease. Despite

theoutliers,PageRankandin-degreeentralityarehighlyorrelated. Figure3.4alsoillustratestheusefulness

oftheLorenzurveforomparingdierentmeasures:itmakesitpossibleto,forinstane,omparerawnumbers

(IDC)tonormalizedones(PageRank).

Fig.3.3. Comparisonofunevennessbetweenin-link-basedandout-link-basedmeasures. (a)ComparisonofICCtoOCC,(b)

ComparisonofIDCtoODC

Betweennessentralityisremarkablyuneven(Figure3.5). Indeed,weimmediatelyseethatmorethan80%

of allnodes havezerobetweenness entrality. The Lorenz urvelearly revealsthat betweenness entrality is

onsiderablylesseventhananyoftheothermeasures disussedhere.

3.3. Disussion. ComparingtheLorenz urvesofthedierent entralitymeasuresreveals aremarkably

diversiedpiture. Betweenness entralityis learly least evenof all. Subsequently, weget degreeentrality,

PageRankandlosenessentrality. TheGinievennessindiesbasiallytellthesamestoryandaresummarized

inTable3.1.

Asatentativeexplanation,wesuggestthatthese dierenesmaybelargelydue to thesmall-worldeet

[26,31℄. Evenmarginalnodesarerelativelyloseto allothers, aountingforminimaldierenesinloseness.

Indeed,thelengthofthediameterthelongestshortestpathisonly11andtheaverageshortestpathlength

only4.12!

Asawhole,the graphtswell intothe bow-tie ororonamodels[6, 7, 11℄,whih were originallydevised

formodelling andexplaining link strutureon theWorldWide Web. Theore ofthemain omponent isthe

LargestStronglyConnetedComponentorLSCC(

N

= 9

,

723

),aomponentinwhihanynodeanbereahed

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Fig.3.4.ComparisonofunevennessbetweenPageRankandin-degreeentrality

Fig.3.5.Unevennessofbetweennessentrality

interesting,seeminglyopposite,eets. Ontheonehand,losenessisinreasedandlosenessentralitybeomes

moreeven. Ontheotherhand,itbringsaboutaveryunevenbetweennessentralitydistribution.

PageRankdistributionismoreeventhanonemightintuitivelyexpet. Thehubshaveahighstatus,whih

is partially transmittedto eah of the nodes they link to. As suh, alarge number of nodes gains a higher

PageRankthanmightbeexpetedfromtheirin-degreeentralityorbetweennessentrality. Indeed,evenifno

shortestpaths passthroughthem, theirPageRankwill still be relativelyhigh. This propertyof PageRankis

verydesirableforrankingWebpages,but maybeunwantedinsomeappliationsofSNA.

4. Conlusions. WehaveshownhowSPARQLanbeusedin proessingsoialSemantiWeb dataina

simpletwo-step methodology, onvertingthe soure graphto a better suited derivedgraph. While SPARQL

isobviouslylesspowerfulthana`real'reasoningengineoradediatedprogram, itis oftensuientandmay

wellprovesimplerandfasterto implement. RDFtoolsaregenerallynotgearedtowardsSNA,althoughFlink

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Ginievennessindexofallentralitymeasuresininreasingorderofevenness

Centralitymeasure G'

Betweennessentrality 0.01

In-degreeentrality 0.12

Degreeentrality(inand out) 0.25

Out-degreeentrality 0.26

PageRank 0.35

In-losenessentrality 0.73

Out-losenessentrality 0.88

Closenessentrality(in andout) 0.94

TheLorenzurveandtheGinievennessindex

G

′

aretwoexellentmethodsforstudyingunevenness. Taking

Agrippa asa onrete example, it anbeseen that unevenness measures may onrm or enfore hypotheses

regardingthenetworktopology. Intheexampledisussed,themassivedierenebetweenbetweennessentrality

andlosenessentralitydistributiononrmsthesmall-worldhypothesisandrevealsthetopologyofthegraph

with asmallnuleus, throughwhih mostotherpaths mustpass. Theexamplealso illustratesthe needfora

widevarietyofentralitymeasures:theyareindeedverydierent(asisobviousfromjustomparingtheLorenz

urves) andeahrevealsadierentaspetofthenetwork.

Mostoftheseresults,suhastheestablishmentofthesmall-worldeet,ouldhavebeenahievedwithout

studying theunevennessof networkproperties. Consequently, theurrentpapershould beregardedasarst

step: it illustrateshowunevennessmeasuresanbeusedto ahieveresultssimilarto existing,well-established

methods. In future researh, we hope to expand upon these resultsby studying a greatervariety of (soial)

networks,inludingdierentlassesofsmall-worldnetworks[2℄.

Aknowledgements. A previous version of this paperwaspresented at the Soial Aspets of the Web

2008Workshop,heldinonjuntionwiththeBIS2008onfereneinInnsbruk. Ithankprof.RonaldRousseau

andtheorganizersandpartiipantstotheWorkshopfortheironstrutiveomments,andprof.RihardPhilips

forprovidingaessto theAgrippadataset.

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Editedby: DominikFlejter,TomaszKazmarek,MarekKowalkiewiz

Reeived: February2nd,2008

Aepted: Marh20th,2008