Abs ac —This pape explo es websi e link s uc u e
conside ing websi es as in e connec ed g aphs and analyzing
hei ea u es as a social ne wo k. Fac o Analysis p o ides he
s a is ical me hodology o adequa ely ex ac he main websi e
p o iles in e ms o hei in e nal s uc u e. Howe e , due o he
la ge numbe o indica o s, a gene ic sea ch o hei op imum
numbe is p oposed, and applied o a case s udy based on 80
Spanish Uni e si y websi es. Resul s p o ide cohe en and
ele an websi e p o iles, and highligh he possibili ies o Gene ic
Algo i hms as a ool o disco e ing new knowledge ela ed o
websi e link s uc u es.
Index Te ms—Link Analysis, Websi e s uc u e, Fac o
Analysis, Gene ic Algo i hms.
I. INTRODUCTION
Link analysis is he quan i a i e s udy o hype links
be ween web pages. I is usually included as pa o
webome ics, which is he quan i a i e analysis o web
phenomena, dealing also wi h web ci a ion analysis, sea ch
engine e alua ion and pu ely desc ip i e s udies o he web
[1], [2]. Web links ha e been hea ily s udied du ing he las
yea s in o de o unde s and he s uc u e and g ow h pa e ns
o he Web [3], and hey ha e been applied o he de elopmen
o page anking algo i hms.. The apid de elopmen
expe ienced by Web links analysis in he heo ies,
echnologies, and me hodologies can be explained by he ac
o being s udied om di e en poin s o iews, like compu e
science, in o ma ion science, communica ions s udies and
sociology [3].
Social ne wo k analysis (SNA) has been equen ly used o
he s udy o link analysis [4], [5]. SNA is a se o esea ch
p ocedu es o iden i ying s uc u es in social sys ems based
on he ela ions among he sys em componen s, also e e ed
o as nodes. In applying SNA me hods o link analysis,
websi es o web-pages a e conside ed he ac o s, ep esen ing
he nodes in he social ne wo k g aph, while links a e modeled
Manusc ip ecei ed Decembe 9, 2009. This wo k has been suppo ed by
he Spanish Minis y o Educa ion and Science (Resea ch P ojec wi h
e e ence DPI2007-60128) and he Conseje ía de Inno ación, Ciencia y
Emp esa (Resea ch P ojec wi h e e ence P07-TIC-02621)..
M. R. Ma ínez To es and B. Palacios a e wi h he Depa men o
Business Adminis a ion and Ma ke ing, Uni e si y o Se ille, Spain).
S. L. To al, and F. Ba e o a e wi h he Elec onic Enginee ing
Depa men , Uni e si y o Se ille, Spain (phone: +34 954481293; ax: +34
954487373; e-mail: o [email protected])..
as he ela ions be ween ac o s, ep esen ing he edges o he
g aph [6]. The esul ing g aph will be a di ec ed g aph because
links a e de ined by an HTML ag wi hin a ma kup ile which
add ess o a new web page se ing he di ec ion o he a c (in
di ec ed g aphs, edges a e called a cs).
The majo i y o s udies a e ocused on he s uc u e o he
web conside ed in a la ge scale. The ela ionships among web
domains ha e been analyzed in he No dic academic web
space [7], o e en in he wo ld web space [8] om he
pe spec i e o SNA. In [9], na ional web domains a e analyzed
a ending o se e al c i e ia, in pa icula , deg ee and anking.
Page epu a ion is ano he opic ela ed o link analysis
equen ly epo ed in he li e a u e. In his case, SNA has also
been applied conside ing he Indeg ee me hod as an
al e na i e o Page ank me hods [10]. Finally, link analysis
h ough SNA has been combined wi h ex analysis o imp o e
web in o ma ion e ie al algo i hms [11].
Al hough Web s uc u e has equen ly been s udied,
compa a i ely li le is known a he websi e le el conce ning
i s s uc u e as an in o ma ion o ganiza ion and access
mechanism. In his pape , an explo a o y s udy o he
iden i ica ion o websi e link s uc u e using ac o analysis is
p oposed. Fo his pu pose, he hype ex s uc u es o eigh y
ins i u ional websi es ha e been ex ac ed bo h a a domain
and a a page le el. The e o e, websi es a e modeled as wo
social ne wo ks. On he i s ne wo k, nodes ep esen
subdomains o ex e nal domains and a cs ep esen he links
among hem. The second one is simila bu conside ing web
pages ins ead o domains o subdomains. A huge numbe o
indica o s ela ed o di e en ea u es o he de i ed ne wo ks
can be compu ed using SNA. Howe e , due o he explo a o y
na u e o his s udy, i is di icul o selec a subse o
indica o s o pe o m ac o analysis, and he al e na i e o
conside ing all possible subse o indica o s is compu a ionally
p ohibi i e. As a solu ion, a gene ic sea ch o an op imum
subse o indica o s using a mul i-objec i e i unc ion is
p oposed. The ob ained esul p o ides new insigh s abou
web si es pa e ns and highligh s he u ili y o gene ic
algo i hms as a ool o new knowledge disco e y.
The es o he pape is s uc u ed as ollows: a b ie
desc ip ion o he me hodology is p o ided in sec ion II. In
pa icula , ne wo k modeling o websi e s uc u e, SNA
ea u es o ex ac ed ne wo ks and ac o analysis
me hodology a e desc ibed. Sec ion III is de o ed o he
applica ion o gene ic algo i hms o he p oblem o ex ac ing
Applica ion o Gene ic Algo i hms o he
Iden i ica ion o Websi e Link S uc u e
M. R. Ma ínez To es, B. Palacios, S. L. To al, Senio Membe , IEEE, and F. Ba e o, Senio
Membe , IEEE
2010 In e na ional Con e ence on Ad ances in Social Ne wo ks Analysis and Mining
978-0-7695-4138-9/10 $26.00 © 2010 IEEE
DOI 10.1109/ASONAM.2010.12
88
2010 In e na ional Con e ence on Ad ances in Social Ne wo ks Analysis and Mining
978-0-7695-4138-9/10 $26.00 © 2010 IEEE
DOI 10.1109/ASONAM.2010.12
88
2010 In e na ional Con e ence on Ad ances in Social Ne wo ks Analysis and Mining
978-0-7695-4138-9/10 $26.00 © 2010 IEEE
DOI 10.1109/ASONAM.2010.12
88
an op imum subse o a iables able o explain he la en
dimensions o websi e s uc u e. The case s udy and esul s a e
discussed in sec ion IV. Finally, conclusions a e de ailed in
sec ion V.
II. WEBSITE STRUCTURE ANALYSIS USING SNA
Ne wo ks ep esen ing web si es a e collec ed s a ing a a
gi en page ( he oo o he ins i u ional web si e) and hen
ollowing he ou links o o he pages. Two di e en kinds o
ne wo ks a e conside ed o each web si e. The i s one is he
domain ne wo k in which nodes ep esen sub domains o
ex e nal domains di e en o he oo domain. A cs ep esen
he link among hem. The second ne wo k is he page ne wo k
con aining all he web pages o he ins i u ional web si e and
he links among hem. Ob iously, bo h ne wo ks a e di ec ed
g aphs and hey can be ex ac ed o he desi ed dep h. In bo h
cases, ne wo k building is limi ed o he oo domain.
Al hough links o o he domains o pages ou side he oo
domain a e conside ed, he ou links om hem will no be
ollowed.
A. SNA
A social ne wo k can be ep esen ed as a g aph G = (V,E)
whe e V deno es a ini e se o e ices and E deno es a ini e
se o edges such ha E ⊆ V × V. Some ne wo k analysis
me hods a e easie o unde s and when g aphs a e
concep ualized as ma ices [12], as shown in Equa ion (1).
o he wise
E i
mVnwhe emM ji
jinnji 0
),(1
,)( ,*,
∈
⎩
⎨
⎧
=== (1)
In case o a alued g aph, eal alued weigh unc ion w(e) is
de ined on he se o edges, i.e. ℜ= xEew )( , and he ma ix is
hen de ined as gi en by Equa ion (2).
o he wise
E i ew
mji
ji 0
),()(
,
∈
⎩
⎨
⎧
= (2)
In he con ex o link analysis, he e e ed domain ne wo k
is a s a -shaped ne wo k wi h he oo domain a he cen e o
he s a and he es o domains linked wi h i . Se e al
indica o s ela ed o he size o he domain ne wo k ha e been
measu ed in e ms o nodes and lines. Typically, ins i u ional
web si es include sub-domains which should be dis inguished
om ex e nal domains. The e o e, his dis inc ion has been
made when conside ing he size in e ms o nodes. Finally, he
densi y and a e age deg ee o he ne wo k ha e also been
conside ed as indica o s. Densi y e e s o he numbe o lines
and deg ee e e s o he numbe o ies in which each e ex is
in ol ed.
The e e ed page ne wo k is a mo e complex ne wo k, wi h a
highe size and a much highe numbe o links han de domain
ne wo k. Consequen ly, a highe numbe o social ne wo k
ea u es can be ex ac ed:
• Size: he numbe o nodes ep esen s he numbe o web
pages and a cs ep esen he in e ela ions among hese web
pages. An impo an pa ame e o be chosen is he dep h o
link co e age when cap u ing web si e in o ma ion. A dep h
o se en has been used in his s udy. This alue is
conside ed su icien o cap u e he essen ial in o ma ion o
websi e s uc u e and is highe han he dep h o i e used in
some p e ious s udies [13].
• Densi y: i is de ined as he numbe o lines in a simple
ne wo k, exp essed as a p opo ion o he maximum possible
numbe o lines. The main p oblem o his de ini ion is ha
i does no ake in o accoun alued lines highe han 1 and i
depends on he ne wo k size. A di e en measu e o densi y
is based on he idea o he deg ee o a node, which is he
numbe o lines inciden wi h i [14]. A highe deg ee o
nodes yields a dense ne wo k, because nodes en e ain mo e
ies, and he a e age deg ee is a non-size dependen measu e
o densi y. As he page ne wo k is a di ec ed g aph, se e al
s a is ical measu es o he ou -deg ee dis ibu ion will be
conside ed. Finally, densi y can be measu ed al e na i ely
using an egocen ic poin o iew; he egocen ic densi y o a
node is he densi y o ies among i s neighbo s [12].
• Componen s: A s ong componen is a maximal s ongly
connec ed subne wo k. A ne wo k is said o be s ongly
connec ed i each pai o e ices is connec ed by a pa h,
aking in o accoun he di ec ion o a cs [12]. In he con ex
o his s udy, componen s allow he iden i ica ion o
connec ed subs uc u es in he gene al web si e.
• K-co es: a k-co e is a sub-ne wo k in which each node has k
deg ee in ha sub-ne wo k. The co e wi h he highes deg ee
is he cen al co e o he ne wo k, de ec ing he se o nodes
whe e he ne wo k es s on. I has been used in [7] o de ec
sub-ne wo ks among No dic academic web si es.
• Dis ance: i is de ined as he numbe o s eps in he sho es
pa h ha connec wo nodes. In he case o web si es, he e is
a clea ly de ined main node which is he oo o he ne wo k.
Consequen ly, i makes sense o measu e he dis ance o
pages o his node.
• Closeness cen aliza ion: i is an index o cen ali y based on
he concep o dis ance. The closeness cen ali y o a node is
calcula ed conside ing he o al dis ance be ween one node
and all o he nodes, whe e la ge dis ances yield lowe
closeness cen ali y sco es. The closeness cen aliza ion is an
index de ined o he whole ne wo k, and i is calcula ed as
he a ia ion in he closeness cen ali y o e ices di ided
by he maximum a ia ion in closeness cen ali y sco es
possible in a ne wo k o he same size [15].
• Be weenness: i is a measu e o cen ali y ha es s on he
idea ha a pe son is mo e cen al i he o she is mo e
impo an as an in e media y in he communica ion ne wo k
[12]. The cen ali y o a node depends on he ex en o which
his node is needed as a link o acili a e he connec ion o
nodes wi hin he ne wo k. Then, hey a e said o de elop a
b oke age ole. I a geodesic is de ined as he sho es pa h
be ween wo nodes, he be weenness cen ali y o a e ex is
he p opo ion o all geodesics be ween pai s o o he
e ices ha include his e ex, and be weenness
cen aliza ion o he ne wo k is he a ia ion in he
be weenness cen ali y o e ices di ided by he maximum
a ia ion in be weenness cen ali y sco es possible in a
ne wo k o he same size. F om he link analysis pe spec i e,
898989
his measu e allows o de ec ga eways connec ing sepa a e
sub ne wo ks [16].
• Pa i ion co ela ion: A pa i ion o a ne wo k is a
classi ica ion o clus e ing o he nodes in he ne wo k such
ha each node is assigned o exac ly one class o clus e [5].
Two impo an pa i ions can be ex ac ed using ne wo k
ea u es p e iously in oduced. The i s one i he k-
neighbou pa i ion, in which nodes a e clus e ed using he
dis ance o he oo node. The second one i he ou -deg ee
pa i ion in which nodes a e clus e ed a ending o hei ou -
deg ee alue. The co ela ion be ween bo h pa i ions is
ela ed o he ex en in which he web si e is ollowing a ee
s uc u e om he oo domain. Two ypes o associa ion
indices a e compu ed: C ame ’s V and Rajski’s in o ma ion
index [12]. C ame ’s V measu es he s a is ical dependence
be ween wo classi ica ions. Rajski’s indices measu e he
deg ee o which he in o ma ion in one classi ica ion is
p ese ed in he o he classi ica ion. Only he symme ical
e sion o Rajski’s indices has been conside ed.
B. Fac o Analysis
Fac o Analysis is a way o i a model o mul i a ia e da a,
es ima ing hei in e dependence. I add esses he p oblem o
analyzing he s uc u e o in e ela ionships among a numbe
o a iables by de ining a se o common unde lying
dimensions, he ac o s, which a e no di ec ly obse able,
segmen ing a sample in o ela i ely homogeneous segmen s
[17]. Because each ac o may a ec se e al a iables in
common, hey a e known as "common ac o s". Each a iable
is assumed o be dependen on a linea combina ion o he
common ac o s, and he coe icien s a e known as loadings
[18].
Ma hema ically, he ac o analysis model exp esses each
desc ip o as a linea combina ion o unde lying common
ac o s 1, 2, . . . , m, wi h an accompanying e o e m o
accoun o ha pa o he a iable ha is unique (no in
common wi h he o he a iables). Fo y1, y2, . . . , yp in any
obse a ion ec o y, he model is as ollows:
pmpmpppp
mm
mm
y
y
y
ελλλμ
ελλλμ
ελλλμ
++++=−
++++=−
++++=−
...
...
...
...
2211
2222212122
1121211111
(3)
Model (3) can be w i en in ma ix no a ion as in Equa ion
(4), whe e Λ is he ac o loadings ma ix.
εμ
+Λ=− y (4)
Ideally, m should be subs an ially smalle han p; o he wise
we ha e no achie ed a pa simonious desc ip ion o he
a iables as unc ions o a ew unde lying ac o s. The
coe icien s λij a e called loadings and se e as weigh s,
showing how each yi indi idually depends on he unde lying
ac o s.
Wi h app op ia e assump ions, λij indica es he impo ance
o he j h ac o j o he i h a iable yi and can be used in
in e p e a ion o j. Fo ins ance, 2 could be in e p e ed by
examining i s coe icien s, λ12, λ22, . . . , λp2.
The la ge loadings ela e 2 o he co esponding y’s. F om
hese y’s, a meaning o desc ip ion o 2 could be in e ed. I is
expec ed he loadings will pa i ion he a iables in o g oups
co esponding o ac o s.
Fac o analysis can be used o ei he explo a o y o
con i ma o y pu poses: explo a o y analyses do no se any a
p io i cons ain s on he es ima ion o ac o s o he numbe o
ac o s o be ex ac ed while con i ma o y analysis does. The
explo a o y na u e o his s udy has se e al implica ions:
• A high numbe o indica o s ela ed o SNA ha e been
ex ac ed o he wo ne wo ks conside ed. The educed
heo e ical backg ound does no allow sc eening ou
unimpo an indica o s be o e analysis ac o begins.
• The numbe o la en ac o s is unknown. Again, he lack o
su icien heo e ical backg ound means ac o s should be
selec ed a ending o he homogenei y o hei indica o s.
Nex sec ion p oposes he use o gene ic algo i hms o
sea ching an op imum solu ion and sol ing hese p oblems.
Once he numbe o ac o s has been de e mined, he nex s ep
is o in e p e hem acco ding o he ac o loadings ma ix.
The es ima ed loadings om an un o a ed ac o analysis i
can usually ha e a complica ed s uc u e. Fo una ely, an
in e es ing p ope y o loadings is ha hey can be mul iplied
by an o hogonal ma ix p ese ing he essen ial p ope ies o
he o iginal loadings. Le T be an a bi a y o hogonal ma ix,
TT’ = I. Inse ing TT’ in o he basic model (4):
ε
μ
+Λ=− TTy ' (5)
Associa ing T wi h Λ and T’ wi h , he model becomes:
εμ
+Λ=− ** y wi h TΛ=Λ* and T '
*= (6)
I can be demons a ed ha he new loadings
Λ
*=
Λ
T
ep oduce he co a iance ma ix [17]. This p ope y is
equen ly used o acili a e he in e p e a ion o ac o s. I we
can achie e a o a ion in which e e y poin is close o an axis,
hen each a iable loads highly on he ac o co esponding o
he axis and has small loadings on he emaining ac o s. In
his case, he e is no ambigui y. The o a ed ac o analysis i
ensu es ha ac o s ep esen unidimensional cons uc s.
III. GENETIC SEARCH OF WEBSITE LATENT DIMENSIONS
A Gene ic Algo i hm (GA) is a compu a ional abs ac ion o
biological e olu ion which can be used o sol e some
op imiza ion p oblems. The echnique was i s in oduced by
Holland [19] o use in adap a i e sys ems. I is an i e a i e
p ocess which applies a se ies o gene ic ope a o s such us
selec ion, c osso e and mu a ion o a popula ion o elemen s.
These elemen s, called ch omosomes o indi iduals, ep esen
possible solu ions o he p oblem. The ini ial popula ion is
andomly selec ed om he solu ion space. Gene ic ope a o s
combine he gene ic in o ma ion o he elemen s o o m new
gene a ions o popula ions. Each ch omosome has an
associa ed i ness alue which quan i ies i s alue as a solu ion
o he p oblem. The ch omosomes compe e o ep oduce based
on hei i ness alues, hus he ch omosomes ep esen ing
be e solu ions ha e a highe chance o su i al. The
c osso e in ol es wo ch omosomes whose po ions a e
swapped. Selec ion acco ding o i ness combined wi h
909090
c osso e gi es he GA i s e olu iona y powe . The GA uses
an eli is s a egy meaning ha he bes indi idual is ca ied
o e o he nex gene a ion so ha we can only imp o e he
solu ion o e he cou se o he gene ic op imiza ion. The
algo i hm s ops when some s opping c i e ions a e sa is ied
[20]. Se e al ques ions should be aking in o accoun when
applying GA:
• Ch omosomal encoding, how o ep esen possible solu ions.
• Fi ness unc ion selec ion. I mus accu a ely ep esen he
alue o he solu ion.
• Pa ame e alues selec ion (popula ion size, numbe o
i e a ions, p obabili ies, e c.)
In his s udy, he use o GA is jus i ied due o i s
explo a o y na u e. Up o 64 indica o s has been ex ac ed
acco ding o he SNA ea u es de ailed in sec ion II.A. The
p oblem o choosing a subse o indica o s leading o
in e p e able la en ac o s is una o dable when ying o
explo e all he possibili ies. The space o possible solu ions is
o med by 264 = 1.8447e+019 possibili ies. Tha means ha we
should pe o m 264 di e en ac o analyses o comple ely
explo e he space o possible solu ions. In his kind o
p oblems, GA can pe o m a guided sea ch o he op imum
solu ion wi h lowe compu a ional cos han explo ing one by
one all he possibili ies.
The i s condi ion o apply GA p ope ly is a good selec ion
o he ch omosomal encoding, which should be alid and
comple e. Ou ch omosomal encoding is cons i u ed by a 64
bina y sequence in which “ones” a e he a iables ha a e
going o be used in ac o analysis, and “ze os” ep esen s
a iables ha a e going o be excluded om his analysis.
Clea ly, he encoding ep esen a ion is comple e, as he 264
possibili ies a e able o be ep esen ed, and alid, as all o
hem can be compu ed.
The nex s ep is he i ness unc ion selec ion. The i ness
unc ion quan i ies he sui abili y o each ch omosome as a
solu ion. Ch omosomes wi h high i ness ha e mo e chance o
being selec ed, passing hei gene ic ma e ial ( ia ep oduc ion
o c osso e ) o he nex gene a ion. The i ness unc ion
p o ides he p essu e o e olu ion owa ds a new gene a ion
wi h ch omosomes o highe i ness han he p e ious ones.
The ch omosome ep esen ing he op imal solu ion should
ha e he maximum i ness alue o he solu ion space, and
nea op imal solu ions should ha e highe i ness alues. In
he con ex o ac o analysis, i is no possible o build a
simple i ness unc ion. Fi ness unc ion should be mul i-
objec i e i ness unc ion conside ing se e al pa ame e s, like
explained a iance, co ela ions and in e p e abili y o he
la en ac o s.
∑
=
++=
k
i
iIn e pc
n
cVa cF
1
3
2
21
1 (7)
• Explained a iance (Va ). Fac o analysis esul s show he
explained a iance by he conside ed ac o s (usually, he
numbe o ac o s is gi en by he numbe o eigen alues o
he co ela ion da a ma ix bigge han 1). The explained
a iance h ough he selec ed numbe o indica o s should be
maximized. Bu i is no he unique pa ame e o be aken
in o accoun . A i ness unc ion equal o he explained
a iance will end o he i ial solu ion o jus conside ing
one indica o . This is due o he ac ha i is easie o
explain he a iance o a da a se when i is o med by a
small numbe o da a.
• Co ela ions be ween a iables ( ∑=
k
ii
n 1
2
/1 ). The a e age
o he sum o he squa ed co ela ion coe icien s be ween
indica o s is used as he second pa o he i ness unc ion.
This e m will end by i sel o he i ial solu ion o
conside ing he whole da a se . I is he e e se s eng h o
he p e ious pa o he i ness unc ion.
• In e p e abili y o ac o s. The hi d pa o he i ness
unc ion penalizes ac o s wi h less han h ee indica o s.
The eason o choosing he alue o 3 is because ac o s
explained wi h less han h ee indica o s a e no conside ed
well-de ined in he li e a u e [17]. This pa o he i ness
unc ion is he mos impo an one as i is p omo ing a
educed numbe o ac o s wi h mo e indica o s, imp o ing
he inal in e p e a ion o he la en ac o s.
C1, C2, and C3 coe icien s a e used o adjus he ela i e
impo ance o he h ee pa s o he i ness unc ion.
Ob iously, he ange o hem is [0,1], wi h he es ic ion o
C1 + C2 + C3 = 1.
The inal decision o GA applica ion e e s o pa ame e
alues selec ion. GA pe o mance may be sensi i e o ce ain
pa ame e alues, pa icula ly he popula ion size, he
equency o ope a o selec ion and he e mina ion c i e ion.
All o hem a y conside ably, and he e is li le o no
documen ed jus i ica ion o hei selec ion. Ne e heless, a
high alue o he popula ion size may educe his sensibili y
o GA pa ame e s. In his pape , popula ion size has been
chosen equal o 10000, wi h a 20% o ep oduc ion a e. The
alue o 10000 is conside ed a good alue o ob ain ichness
gene ic con en . These alues a e ypical in he li e a u e abou
GA [20], [21].
IV. CASE STUDY
The gene ic sea ch o web si es la en dimensions has been
applied o 80 Spanish Uni e si y web si es. All o hem a e
included in he Webome ics Ranking o Wo ld Uni e si ies
(www.webome ics.o g), whe e mo e han 6000 uni e si ies
all o e he wo ld a e so ed acco ding o size and isibili y.
Table I lis s he oo domains o he conside ed web si es.
They co e almos he whole ange o Webome ics Ranking,
and exhibi a a ie y o size in e m o domains and web
pages. Table II summa izes some desc ip i e s a is ics. The
second column shows ha mo e han 718.000 web pages and
mo e han ou million ou links ha e been conside ed. Figu e
1and Figu e 2 shows he pa icula case o he domain and
page ne wo k, espec i ely, co esponding o he pa icula
case o he Uni e si y o Se ille. Fo each web si e, wo
s a ing ne wo ks ha e been collec ed: he domain ne wo k
and he page ne wo k.
919191
Table I. Lis o conside ed web si es.
Spanish Uni e si ies web si es
h p://www.ucm.es/ h p://www.ual.es/
h p://www.upc.edu/ h p://www.udl.es/
h p://www.upm.es/ h p://www.ujaen.es/
h p://www.uab.es/ h p://www.umh.es/
h p://www.ehu.es/ h p://www.deus o.es/
h p://www.ub.edu/ h p://www.una a a.es/
h p://www.us.es/ h p://www.upc .es/
h p://www.up .es/ h p://www.upo.es/
h p://www.um.es/ h p://www.ie.edu/
h p://www.ug .es/ h p://www.upcomillas.es/
h p://www.ua.es/ h p://www.ceu.es/
h p://www.u igo.es/ h p://www.iese.edu/
h p://www.u .es/ h p://www.ubu.es/
h p://www.uam.es/ h p://www.u .ne /
h p://www.usal.es/ h p://www.uni ioja.es/
h p://www.uji.es/ h p://www.uem.es/
h p://www.uniza .es/ h p://www.esade.edu/
h p://www.usc.es/ h p://www.ucam.edu/
h p://www.uib.es/ca/ h p://www.mond agon.edu/
h p://www.uclm.es/ h p://www.u ic.es/
h p://po al.uned.es/ h p://www.ce .es/
h p://www.u a.es/ h p://www.uch.ceu.es/
h p://www.up .edu/ h p://www.neb ija.com/
h p://www.una .es/ h p://www.uic.es/
h p://www.uc3m.es/ h p://www.u l.es/
h p://www.unio i.es/ h p://www.esdi.es/
h p://www.uma.es/ h p://www.uax.es/
h p://www.uco.es/ h p://www. i es.o g/
h p://www.ull.es/ h p://www.uimp.es/
h p://www.udc.es/ h p://www.ucjc.edu/
h p://www.unex.es/ h ps://www.uc .es/
h p://www.uah.es/ h p://www.uspceu.com/
h p://www.uoc.edu/ h p://www.cesdonbosco.com/
h p://www.udg.edu/ h p://www.u .es/
h p://www.ulpgc.es/ h p://www.esic.es/
h p://www.unican.es/ h p://www.cepade.es/
h p://www.unileon.es/ h p://www.eoi.es/po al/
h p://www.u jc.es/ h p://www.esmuc.ne /
h p://www.uca.es/ h p://www.udima.es/
h p://www.uhu.es/ h p://www.eupm .es/
Table II. Websi es Desc ip i e s a is ics.
Sum Mean SD
Subdomains 2438 30,47 38,10
Ex . domains 30500 381,25 580,32
Pages 718272 8978,40 15334,01
Ou -links 4429231 55365,38 73290,17
The social ne wo k ea u es o sec ion II.A ha e been
measu ed, conside ing in some cases he whole ne wo k, and
in some cases he subne wo ks excluding nodes wi h 0 ou -
deg ee o subne wo ks wi h k>1 co es. As a esul , 64
indica o s ha e been ob ained.
Figu e 1. Uni e si y o Se ille domain ne wo k.
Figu e 2. Uni e si y o Se ille page ne wo k.
A. Da a Analysis
GA has been applied o ob ain an op imum subse o
indica o s able o iden i y web si e p o iles acco ding o hei
link s uc u e. The cos unc ion ollow he gene al s uc u e
de ined in sec ion III bu conside ing he alues c1=0,15,
c2=0,1 and c3= 0,75. No ice ha in e p e abili y o ac o s has
been clea ly o e weighed. This s a egy seems easonable,
since ac o s wi h less han h ee indica o s a e no admissible
in ac o analysis. Besides, in e p e abili y guides GA owa ds
a educed numbe o ac o s, which is also easonable o ind
ac o s wi h clea and sepa a e meanings.
Beginning wi h an ini ial andomly gene a ed popula ion,
GA has con e ged a e 30 gene a ions, wi h an explained
a iance o 77,10 %, and 25 indica o s g ouped in 6 ac o s.
All o hem include a leas h ee indica o s, and hei
meaning, using Va imax o a ion, a e in e p e able. Time
equi ed by gene ic algo i hm execu ion is 4.822,49 seconds
(80,37 minu es). This alue is much smalle han he
al e na i e op ion o explo ing he whole solu ion space.
Taking in o accoun ha each ac o analysis equi es 12.9 ms,
he 264 = 1.8447e+019 possibili ies o he solu ion space
would equi e millions o yea s. The selec ed subse o
indica o s is lis ed in Table III. In pa icula , he indica o s
desc ip ion and he ne wo k o e which i is calcula ed a e
929292

de ailed.
Table III. Selec ed subse o indica o s.
Indica o Ne wo k
I1 Ex e nal domains Domain Ne .
I2 A e age deg ee Domain Ne .
I3 Densi y Domain Ne .
I4 Numbe o pages Page Ne .
I5 Numbe o pages in he las
le el (dep h o 7) Page Ne .
I6 Numbe o no- e u ning pages
(excluding las le el) Page Ne .
I7 Ou -deg ee s anda d de ia ion Page Ne .
I8 Numbe o s ong componen s Page Ne .
I9 % o pages included in s ong
componen s Page Ne .
I10 K-co e including he
maximum numbe o pages Page Ne .
I11 A e age alue o closeness
cen ali y Page Ne .
I12 S anda d de ia ion o
closeness cen ali y Page Ne .
I13 Numbe o pages Page Ne . exclu-
ding ou -deg ee=0
I14 Be weeness cen aliza ion Page Ne .
I15 S anda d de ia ion o
egocen ic densi y Page Ne .
I16 A e age alue o nodes
be weeness cen ali y
Page Ne wo k o
k-co es, k>0
I17 S anda d de ia ion o e ices
be weeness cen ali y
Page Ne wo k o
k-co es, k>0
I18 A e age alue o egocen ic
densi y
Page Ne wo k o
k-co es, k>0
I19 A e age alue o e ices
be weeness cen ali y
Page Ne . exclu-
ding ou -deg ee=0
I20 A e age alue o egocen ic
densi y
Page Ne . exclu-
ding ou -deg ee=0
I21 Numbe o e ices
de eloping a b oke age ole
Page Ne . exclu-
ding ou -deg ee=0
I22 S anda d de ia ion o
b oke age oles
Page Ne . exclu-
ding ou -deg ee=0
I23
C ame ’s V index o pa i ion
co ela ion (ou -deg ee, k-
neighbou )
Page Ne .
I24
Rajski’s index o pa i ion
co ela ion (ou -deg ee, k-
neighbou )
Page Ne .
I25
Rajski’s index o pa i ion
co ela ion (ou -deg ee, k-
neighbou )
Page Ne . exclu-
ding ou -deg ee=0
The esul s om ac o analysis using he se o a iables
selec ed by he gene ic algo i hm a e de ailed in Table IV.
Usually, a numbe o ac o s equal o he numbe o
eigen alues highe han 1 is selec ed [17]. Consequen ly, up o
6 la en ac o s can be dis inguished as esul o ac o
analysis.
Table IV. Explained a iance o esul ing ac o analysis.
Fac o
Eigen alues
Value %
a iance % cumula i e
1 7,990 31,962 31,962
2 3,852 15,407 47,369
3 2,911 11,646 59,015
4 1,857 7,427 66,442
5 1,656 6,624 73,065
6 1,010 4,039 77,104
7 ,833 3,333 80,437
8 ,741 2,964 83,401
9 ,636 2,545 85,946
10 ,532 2,127 88,073
11 ,497 1,990 90,063
12 ,429 1,716 91,779
13 ,386 1,545 93,324
14 ,330 1,318 94,642
15 ,279 1,116 95,758
16 ,249 ,995 96,753
17 ,193 ,772 97,524
18 ,172 ,689 98,213
19 ,143 ,570 98,784
20 ,124 ,496 99,280
21 ,078 ,311 99,591
22 ,045 ,182 99,773
23 ,032 ,129 99,902
24 ,017 ,069 99,971
25 ,007 ,029 100,000
The indica o s associa ed o each ac o a e ob ained om
he ac o loadings using a Va imax o a ion. All he indica o s
associa ed in his way wi h he same ac o a e hypo hesized o
sha e a common meaning ha he analys should disco e .
On he o he hand, ac o sco es a e used o ca ego ize he
o iginal sample o Uni e si ies, which can be app oxima ed o
one o he iden i ied la en ac o s. An analysis o a iance
(ANOVA) has been pe o med o check he null hypo hesis o
equal popula ion means. These null hypo heses ha e been
ejec ed in all he cases wi h a signi icance alue below 0,05.
Using he in o ma ion o he ac o loadings as well as he
mean alues o he ca ego ized g oups o Uni e si ies, he
ollowing websi es s uc u e pa e ns can be highligh ed
(Table V):
Fac o 1 ep esen s a dis ibu ed s uc u e o he websi e,
wi h a lo o nodes de eloping a be weenness ole. The high
alue o pa i ion co ela ions also suppo s he dis ibu ed
s uc u e wi h lowe and in e media e le el pages (nea he
oo domain) ac ing as di ec o ies o in o ma ion and highe
le el pages ( a om he oo domain) p o iding mo e de ailed
939393
in o ma ion.
Fac o 2 ep esen s a mo e cen alized s uc u e in he sense
o dis ance o he oo domain. The e is a co e o highly
in e connec ed pages, bu he in o ma ion is also sp ead ou as
we mo e owa d deepe le els in he s uc u e.
Fac o 3 e e s o an egocen ic s uc u e, whe e he global
ne wo k could be conside ed as he sum o mo e o less
independen subne wo ks.
Fac o 4 conside s la ge web si es. The numbe o pages
g ows geome ically wi h he dep h le el, so i is necessa y a
long na iga ion p ocess o achie e he desi ed in o ma ion.
Fac o 5 ep esen s smalle web si es, whe e a g ea amoun
o in o ma ion is p o ided using ex e nal e e ences o he web
si es. This idea is suppo ed by he high alue o non- e u ning
pages excluding pages loca ed in he las le el.
Finally, ac o 6 ep esen s web si e wi h a s uc u e
domina ed by one subne wo k, con aining he mos ele an
in o ma ion.
Table V. Iden i ied ac o s.
Desc ip ion Loading
F1
I2 A e age deg ee -0,724
I16 A e age alue o nodes
be weeness cen ali y 0,903
I17 S anda d de ia ion o e ices
be weeness cen ali y 0,884
I19 A e age alue o e ices
be weeness cen ali y 0,839
I23
C ame ’s V index o pa i ion
co ela ion (ou -deg ee, k-
neighbou )
0,703
I25
Rajski’s index o pa i ion
co ela ion (ou -deg ee, k-
neighbou )
0,746
F2
I9 % o pages included in s ong
componen s 0,722
I11 A e age alue o closeness
cen ali y 0,924
I12 S anda d de ia ion o closeness
cen ali y 0,718
I14 Be weeness cen aliza ion 0,826
I24
Rajski’s index o pa i ion
co ela ion (ou -deg ee, k-
neighbou )
0,578
F3
I15 S anda d de ia ion o egocen ic
densi y 0,763
I18 A e age alue o egocen ic
densi y 0,895
I20 A e age alue o egocen ic
densi y 0,875
F4
I4 Numbe o pages 0,900
I5 Numbe o pages in he las le el
(dep h o 7) 0,928
I13 Numbe o pages 0,661
Desc ip ion Loading
I21 Numbe o e ices de eloping a
b oke age ole 0,510
F5
I1 Ex e nal domains 0,852
I6 Numbe o no- e u ning pages
(excluding las le el) 0,647
I8 Numbe o s ong componen s 0,831
F6
I7 Ou -deg ee s anda d de ia ion 0,786
I10 K-co e including he maximum
numbe o pages 0,633
I22 S anda d de ia ion o b oke age
oles 0,635
Basically, he iden i ied p o iles o web si e s uc u es
espond o wo basic s a egies when deciding hei inal
s uc u e [22]. The i s s a egy consis s o o e ing a s uc u e
which makes sense o he inal use . In his sense, web si es
sac i ices accessibili y o in o ma ion looking o a mo e
s uc u ed na iga ion scheme. Fac o s 1, 3 and 4 could be
included in his s a egy. The al e na i e op ion consis s o
educing big s uc u es unde he assump ion ha use
pe o mance is op imal when b ead h and dep h o Websi e is
kep o a mode a e le el [22]. This is he s a egy o p o iles
iden i ied by ac o s 5 and 6. Finally, ac o 2 could be
conside ed as a mix u e o bo h s a egies.
V. CONCLUSION
This pape has de eloped a ool o iden i ying websi e link
s uc u es conside ing websi es as social ne wo ks. The use o
e olu iona y compu a ion echniques has allowed ex ac ing
he main p o iles in he pa icula case o ins i u ional websi es
om Spanish Uni e si ies. Ob ained esul s ag ee wi h he
gene al ules o websi e designs p oposed in he li e a u e.
Al hough he s udy is limi ed o Spanish Uni e si ies
Websi es, hey cons i u e a ich enough sample among he
Webome ics Ranking o Wo ld Uni e si ies. This s udy could
be ex ended o o he ins i u ional web si es o alida e he
ob ained esul s.
ACKNOWLEDGMENT
This wo k has been suppo ed by he Spanish Minis y o
Educa ion and Science (Resea ch P ojec wi h e e ence
DPI2007-60128) and he Conseje ía de Inno ación, Ciencia y
Emp esa (Resea ch P ojec wi h e e ence P07-TIC-02621).
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