Kazemila i, Mansoo eh; Š eimikienė, Dalia
A icle
Topological ne wo k analysis and i s applica ion on
e ealing dimensions o s uden sa is ac ion unde he
COVID-19 pandemic
Con empo a y Economics
P o ided in Coope a ion wi h:
VIZJA Uni e si y, Wa saw
Sugges ed Ci a ion: Kazemila i, Mansoo eh; Š eimikienė, Dalia (2024) : Topological ne wo k analysis
and i s applica ion on e ealing dimensions o s uden sa is ac ion unde he COVID-19 pandemic,
Con empo a y Economics, ISSN 2300-8814, Uni e si y o Economics and Human Sciences in
Wa saw, Wa saw, Vol. 18, Iss. 4, pp. 475-485,
h ps://doi.o g/10.5709/ce.1897-9254.550
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/312966
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h ps://c ea i ecommons.o g/licenses/by/4.0/
www.ce. izja.pl
475
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License.
Topological ne wo k analysis is an ad anced ool o e ealing cus ome sa is ac ion in ma ke ing esea ch
and o he ields. The uni e si y sec o plays a i al and compe i i e ole in con ibu ing o a coun y's de el-
opmen . S uden s a e ega ded no only as a sou ce o income bu also as a key c i e ion o a aining he
ision and mission o eaching in e na ional s anda ds o uni e si ies. S uden sa is ac ion is cha ac e ized as a
comp ehensi e assessmen o he educa ional expe ience, o med by compa ing ini ial expec a ions wi h he
pe cei ed pe o mance ollowing he comple ion o he educa ional cycle. The assessmen o s uden s' sa is-
ac ion is a con inuous p ocess ha demands ongoing moni o ing o main ain high anks o quali y. Because
o he dis u bance caused by he COVID-19 pandemic, academic ins i u ions adjus ed hei cu icula and de-
li e y me hods o align wi h he eme ging no ms o online lea ning. Assessing s uden sa is ac ion is c i ical o
de e mining how e ec i e he online eaching me hod is. To unde s and he key ac o s in luencing s uden
sa is ac ion, he s udy examines he in e connec ions among h ee dimensions (24 i ems) by using co ela ion
ne wo k analysis and Minimal Spanning T ee (MST) me hods. Dioid algeb a simpli ies he MST sea ch in o a
single s ep by cons uc ing a con e ging sequence, elimina ing he need o con e gence e i ica ion, and
cen ali y measu es a e employed o in e p e and p esen he ne wo k esul s. The indings sugges a mo e
p ecise conclusion: To enhance s uden sa is ac ion, i is impe a i e o alloca e g ea e ocus owa ds e ining
eaching me hodologies, enhancing he pandemic s udy p og am, and imp o ing he cou se con en o
online educa ion.
1. In oduc ion1. In oduc ion
Economic ad ancemen can lead o an inc ease
in educa ional ade, as coun ies ha e demon-
s a ed he c ucial ole o educa ion in accele a ing
economic g ow h. The p og ess o de elopmen im-
pac s he g owing in e es in educa ion.
The desi e o ad anced educa ion is expec ed
o pe sis , and go e nmen s emb ace educa ional
ade wi h he goal o o e ing supe io quali y edu-
ca ion and a mo e ex ensi e ange o s udy op ions
(Quispe-P ie o e al., 2021).
Acco ding o Ng and Fo bes (2009), i is e iden
ha ega dless o uni e si ies' pe cep ions o s u-
den s' desi es, s uden s a e he consume s o ad-
anced educa ion, and hei con en men wi h he
uni e si y expe ience holds signi ican impo ance.
In oday's highly compe i i e landscape o in e na-
Topological Ne wo k Analysis and i s Applica ion on
Re ealing Dimensions o S uden Sa is ac ion Unde
he COVID-19 Pandemic
ABSTRACT
I23, C55, I12, D85.
KEY WORDS:
JEL Classi ica ion:
opological ne wo k analysis, dioid algeb a, s uden sa is ac ion, online lea ning.
1
Depa men o Ma hema ics and Compu e Science, Uni e si y o Technology, Papua New Guinea
2
Vy au as Magnus Uni e si y, Kaunas, Li huania
Co espondence conce ning his a icle should be add essed o:
Dalia S eimikiene, Vy au as Magnus Uni e si y, Kaunas, Li huania.
E-mail: [email p o ec ed]
Mansoo eh Kazemila i1, Dalia S eimikiene2
P ima y submission: 22.02.2024 | Final accep ance: 05.06.2024
476
Mansoo eh Kazemila i, Dalia S eimikiene
10.5709/ce.1897-9254.550DOI: CONTEMPORARY ECONOMICS
Vol. 18 Issue 4 475-4852024
ional educa ion, g asping he elemen s ha im-
pac s uden sa is ac ion could enable educa ional
ins i u ions and go e nmen al bodies o enhance
and e ol e hei o e ings. This imp o emen aims
o be e mee he needs o p ospec i e s uden s,
ul ima ely a ac ing a la ge s uden popula ion
(Songsa hapho n e al., 2014).
Due o he eme gence o he COVID-19 pandem-
ic, he e has been a signi ican ans o ma ion in
he educa ion sys em, expe iencing a p onounced
shi om adi ional on-campus ins uc ion o
i ual eaching acili a ed by online lea ning and
digi al echnologies. This unexpec ed change has
p esen ed nume ous challenges o s uden s, each-
e s, and academic ins i u ions. A key challenge is
he implemen a ion o online educa ion sys ems o
supe io quali y, inco po a ing he la es echnolo-
gies in online lea ning, and ensu ing he deli e y
o high-calibe educa ion (Bu e al., 2022; Ko n-
pi ack & Sawmong, 2022; Mohd Sa a e al., 2020).
Despi e he ine i abili y o e-lea ning becom-
ing he new no m in educa ional ins i u ions, he
ab up ansi ion aises conce ns abou he qual-
i y o deli e y, in as uc u e p epa edness, and
he adequacy o aining (Mohd Sa a e al., 2020).
While many s udies ha e examined di e en ace s
o e-lea ning sa is ac ion, i is essen ial o alida e
hese heo ies in he con ex o he e-lea ning ex-
pe ience du ing c ises. Addi ionally, he e is a need
o explo e he success ac o s o implemen ing e-
lea ning in such si ua ions, conside ing he exis -
ing heo e ical amewo ks (Bu , Mahmood, &
Saleem, 2022).
Co és, e al. (2019) asse ha he s uden should
no be pe cei ed me ely as a clien o a passi e e-
cipien o se ices. Acco ding o hei pe spec i e,
conduc ing esea ch on s uden sa is ac ion is a
meaning ul con ibu ion o enhancing he o e all
quali y o educa ional se ices. This app oach em-
phasizes he need o ongoing imp o emen s in
educa ional se ices. The e o e, i is essen ial o ac-
i ely seek eedback om s uden s ega ding hei
sa is ac ion wi h he educa ional ins i u ion's qual-
i y and compe i i e s anda ds (Sánchez Quin e o,
2018; Quispe-P ie o e al., 2021;).
The uni e si y mus assess he dimensions o s u-
den s' sa is ac ion and he ac o s a ec ing i . The
p esen esea ch is he i s one ha conside s he
dimensions o s uden s' sa is ac ion in online lea n-
ing by using he applica ion o algeb aic s uc u e
in a co ela ion ne wo k-based app oach as a heo-
e ical basis o analyse ac o s' beha iou .
The p ima y aims o his s udy a e: (a) o pin-
poin ac o s ha posi i ely impac s uden sa is ac-
ion du ing he COVID-19 pandemic, (b) o assess
s uden s' sa is ac ion wi h online educa ion, and (c)
o o e ecommenda ions o bo h uni e si ies and
go e nmen s akeholde s.
This quan i a i e s udy employs a sa is ac ion
su ey as i s p ima y me hod o da a collec ion,
ocusing on e alua ing he ac o s in luencing he
sa is ac ion o s uden s a Shi az Uni e si y in I an.
A opological analysis me hod is employed o assis
in in e p e ing he exis ing ela ionships among all
ac o s and iden i ying he in luen ial ac o s con-
ibu ing o s uden s’ sa is ac ion.
2. Li e a u e Re iew2. Li e a u e Re iew
2.1. P e ious Resea ch on S uden s’ Sa is ac-
ion Du ing he COVID-19
The quali y o se ice a he uni e si y bene i s
om s uden s' inpu ega ding eaching me hods,
lea ning en i onmen , in e ac ion, and hei
mo i a ion o s udy. These aspec s, whe he in e nal
o ex e nal, play a signi ican ole in shaping an
indi idual's academic sa is ac ion (Me ino-So o,
2017).
Rosa io Rod íguez e al. (2020) in oduce a
p ac ical model o e alua ing sa is ac ion using
a c oss-sec ional, non-expe imen al, explo a o y,
and desc ip i e design. Thei esea ch, in ol ing
167 s uden s om 17 uni e si ies in Pue o Rico,
o e s aluable insigh s in o me hodologies o
assessing sa is ac ion (Rosa io-Rod íguez e al.,
2020).
Mohd Sa a e al. (2020) in es iga ed how IT
cha ac e is ics in luence s uden s' sa is ac ion wi h
online lea ning du ing he lockdown pe iod o he
COVID-19 pandemic. They conduc ed an online
su ey in Malaysia, ga he ing da a om a sample
o 470 s uden s selec ed h ough con enience
sampling, as uni e si ies ansi ioned hei classes
o i ual modali y (Mohd Sa a e al., 2020).
www.ce. izja.pl
477
Topological Ne wo k Analysis and i s Applica ion on Re ealing Dimensions o S uden Sa is ac ion Unde he COVID-19 Pandemic
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License.
Quispe-P ie o e al. (2021) employed sys ems
concep s in hei in es iga ion o explo e s uden s'
expe iences and sa is ac ion wi h he online
lea ning pla o m om he iewpoin o s uden s
wi hin he sample o h ee highe educa ion
ins i u ions in hei s udy.
These s udies pa e he way o examining ab up
shi s in educa ional modali y, speci ically he
ansi ion om adi ional class oom o online
app oaches, and hei e ec s on s uden s, as
highligh ed by Rosa io-Rod íguez e al. (2020).
A e e iewing he li e a u e and in line wi h
he s udy by Quispe-P ie o e al. (2021), i was
ound ha s uden sa is ac ion is linked o h ee
main dimensions: (a) sa is ac ion wi h suppo and
adap a ion in online en i onmen s, (b) sa is ac ion
wi h in e ac ion in online class ooms, and (c)
sa is ac ion wi h he p og ession o he academic
p og am (Quispe-P ie o e al., 2021).
2.2. Algeb aic S uc u e o Dioid Algeb a
Classical algeb aic s uc u es like g oups, ings,
and ields ha e been ounda ional o he majo -
i y o ad ancemen s in Ma hema ics and Physics
o e he pas h ee o ou cen u ies. Howe e , he
scope o ma hema ical models has signi ican ly ex-
panded due o he eme gence o new app oaches
like Fuzzy Se heo y and he inc easing need o
p oblem-sol ing echniques in g aphs and Ope a-
ions Resea ch applica ions (Gond an & Minoux,
2008). O e he las h ee o ou decades, di e en
algeb aic s uc u es like semi ings and dioids ha e
been ho oughly in es iga ed and ha e become
signi ican ools and models pe aining o uzzy
se s and hei uses o add essing a wide ange o
non-classical p oblems in a eas such as ma hema i-
cal physics, decision analysis, ope a ions esea ch,
uzzy se heo y, and au oma ic con ol (Gond an
& Minoux, 2007). Many esea ch wo ks explici ly
men ion he semi ing s uc u e, whe e he canoni-
cal o de p ope y is p esen in almos all ins ances,
canonical o de p ope y almos always p esen ,
o en due o he idempo ency o . Consequen ly,
many algeb aic indings in he li e a u e on Fuzzy
Se s can be unde s ood as p ope ies o dioids
(Gond ana & Minoux, 2007).
A signi ican example is he elemen a y uzzy
algeb a ([0,1], max, min), which bea s a close e-
la ionship o he algeb aic s uc u e ( , max, min).
This s uc u e has been e e ed o by a ious
names in he li e a u e, including 'Minimax Alge-
b a' (Ga alec, 2002), 'Bo leneck Algeb a' (Cech-
lá o á, 2003), 'Fuzzy Algeb a' (Cechlá o á, 1995),
and 'MV-Algeb a' (K oupa, 2006).
P ima y sou ces o semi ings include Hebisch
and Weine (1998) and Golan (1999, 2013). Gon-
d an and Minoux began a ho ough examina ion o
dioids, a subse o semi ings dis inguished by hei
canonical o de ing in ela ion o addi ion, wi h ini-
ial esea ch in 1978 and 1984, ollowed by u he
de elopmen s in 2001. In an a bi a y semi ing (D,
, ), he se D is de ined wi h wo ope a ions: "ad-
di ion" ( ) and "mul iplica ion" ( ), bo h o which
a e closed ope a ions. The s anda d no a ion is
= (D, , ), whe e o , we de ine
a b = min {a,b} and a b = max {a,b}. As such,
(D, , ) akes on he s uc u e o a canonically
o de ed semi ing, e e ed o as a dioid.
In b oade e ms, i should be no ed ha he max
and min ope a ions, which p o ide he se o eals
wi h he s uc u e o a canonically o de ed monoid,
na u ally eme ge in many algeb aic models, lead-
ing o nume ous applica ions o dioid s uc u es.
In some no able ins ances in ol ing di e en ypes
o dioids, ( , min, +) and ( , max, min) a e used
as na u al amewo ks o add essing he maxi-
mum o minimum capaci y pa h p oblem, which
is closely linked o he maximum/minimum weigh
spanning ee p oblem (Gond an, 1975, Pan & Lei ,
1989).
In his pape , we ho oughly in es iga e he ap-
plica ion o algeb aic s uc u es in he minimum
weigh spanning ee. By de ining dioid algeb a,
we s anda dize minimum spanning ee p ob-
lems based on dis ance ma ices and apply hem
o he ne wo k o s uden sa is ac ion dimensions.
This app oach in eg a es he indings o Djauha i
(2017), who esea ched his opic.
3. Resea ch Me hodology3. Resea ch Me hodology
Ne wo k analysis ocuses on moni o ing sub le
changes as he sys em e ol es and measu ing he
signi icance o each ac o in he complex sys em.
When dealing wi h in e connec ed i ems o g asp
478
Mansoo eh Kazemila i, Dalia S eimikiene
10.5709/ce.1897-9254.550DOI: CONTEMPORARY ECONOMICS
Vol. 18 Issue 4 475-4852024
he ue beha io o each dimension, ne wo k anal-
ysis can be u ilized o iden i y he mos in luen ial
i ems (Sha i e al., 2012). This is achie ed h ough
es ablished me hods such as co ela ion ne wo k
analysis and he MST.
Ne wo k analysis s a s wi h a co ela ion ma-
ix. A co ela ion ma ix is able o show ha e-
la ionship clea ly and concisely. I is wieldy used
o quan i ying he in e ac ion among objec s
(Ba abási, 2009; Boccale i e al., 2006; Do ogo -
se & Mendes, 2002). A co ela ion ne wo k-based
app oach is a new me hod ha will help classi y
and u ilize he signi ican in o ma ion included
in he ma ix. The ela ionship be ween ac o s
is cons uc ed in he o m o a ne wo k isually,
which is ex ac ed by he MST based on co ela-
ions ma ix. The e o e, de ined simila i y measu e
based on co ela ion is an ini ial poin o u he
ne wo k analysis.
The i s subsec ion concen a es on ecognizing
he ac o s o s uden sa is ac ion as he p ima y
conside a ion.
3.1. Da a Collec ion
A li e a u e e iew e eals ha s uden sa is ac ion
leads o h ee beha io al in en ions: (i) sa is ac ion wi h
suppo and adjus men o he i ual en i onmen , (ii)
sa is ac ion wi h he in e ac ion in online class ooms,
and (iii) sa is ac ion wi h he s udy p og am de elop-
men . To assess s uden sa is ac ion in online lea ning
du ing COVID-19, wen y- ou i ems we e de eloped
based on hese h ee beha io al in en ions.
The s udy includes unde g adua e s uden s a Shi az
uni e si y who a e speci ically in hei hi d and ou h
yea s o s udy. The ques ionnai e comp ises 24 cha -
ac e is ics o ganized in o h ee dimensions o s uden
sa is ac ion ac o s. O hese, he ini ial 10 pe ain o
sa is ac ion conce ning suppo and adap a ion o he
i ual en i onmen . The ollowing eigh ques ions o-
cus on sa is ac ion wi h in e ac ion in he i ual class-
oom, and he subsequen se en ques ions add ess sa -
is ac ion wi h he de elopmen o he s udy p og am.
Table 1 p o ides a de ailed lis o hese 24 a ibu es.
Su ey pa icipan s answe ed 24 ques ions ha
e alua ed hei sa is ac ion wi h he eaching-lea ning
p ocess. The assessmen u ilized a Like scale wi h i e
op ions: om Ve y Dissa is ied o Ve y Sa is ied.
3.2. Ne wo k Cons uc ion and in o ma ion
il e ing
Be o e es ablishing a complica ed ne wo k, we i s
s udy abou he ela ionship among objec s. In a ne -
wo k-based app oach, a simila i y measu e is used o
in es iga e ne wo k p ope ies using a ma ix, wi h a
pa icula ocus on simila i y-based ne wo ks. These
ne wo ks employ a simila i y measu e such as lin-
ea o Pea son's co ela ion ρ
ij
be ween objec s i and j
(Cono e , 1971; Hauke & Kossowski, 2011; Tan e al.,
2004). The basic o malism o he c oss-co ela ion
ma ix in ol es he de ailed ep esen a ion o wo a i-
ables.
Le X be a andom ec o o dimension p ha ing posi-
i e de ini e co a iance ma ix ∑ = (σ
ij
). The co ela ion
coe icien be ween componen s o X, speci ically he
i- h and j- h componen s, is gi en by:
The coe icien ρ
ij
quan i ies he deg ee o linea
ela ionship be ween he i- h and j- h a iables. By
de ini ion, |ρ
ij
|≤1 , and
Due o his p ope y, ρ
ij
is commonly ega ded as
a na u al measu e o linea dependence among hose
a iables. Now le and be a an-
dom sample o size n d awn om X. The sample co a i-
ance ma ix is S. The ma ix S=(s
ij
) is he sample e sion
o ∑. Thus, he sample co ela ion coe icien be ween
he i- h and j- h a iables is .
ij
is he maximum
likelihood es ima e o ρ
ij
. In his case, ρ
ij
=0 i and only
i bo h i- h and j- h a iable a e independen . Fu he -
mo e, i Ω=(ρ
ij
) ep esen s he popula ion co ela ion
ma ix, i s sample e sion is R=(
ij
).
The co ela ion coe icien be ween i- h and j- h
a iables is calcula ed by ρ
ij
o a pai o X
i
and X
j
i ems.
Co ela ion coe icien ρ
ij
o all pai s o i ems o m a
n × n symme ic ma ix wi h diagonal elemen s equal
o 1. This c oss-co ela ion ma ix shows he deg ee o
co ela ion be ween all ac o s.
Now, wi h all he needed in o ma ion, one can c e-
a e an MST g aph o all in es iga ed ac o s. Fi s , one
www.ce. izja.pl
479
Topological Ne wo k Analysis and i s Applica ion on Re ealing Dimensions o S uden Sa is ac ion Unde he COVID-19 Pandemic
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License.
Table 1
Th ee Dimensions and Fac o s o S uden Sa is ac ion in Online Lea ning Du ing COVID-19
1. SATISFACTION WITH SUPPORT AND ADAPTATION TO ONLINE LEARNING
SA1 Uni e si y S a egies Pandemic Managemen Assessmen : E alua ing S uden Sa is ac ion
wi h Uni e si y Response S a egies
SA2 Online Technology Technology Suppo Sa is ac ion: E alua ing S uden Con en men wi h
Uni e si y Assis ance in Online Technology
SA3 Online Educa ion Vi ual Lea ning Lec u e Commi men Assessmen : E alua ing S u-
den Sa is ac ion wi h Ins uc o Dedica ion in Online Educa ion
SA4 Adap a ion Academic Adap a ion Sa is ac ion: E alua ing S uden Con en men
wi h Tu o s' and P o esso s' Adjus men s Amid he Pandemic
SA5 Suppo Se ices Beyond IT Suppo : E alua ing S uden Sa is ac ion wi h Di e se Uni-
e si y Suppo Se ices
SA6 Technological Facili a ion Technological Facili a ion: E alua ing S uden Sa is ac ion wi h Lec u -
e s' use o Technology o Lea ning
SA7 Ca ee Lec u e s' Pandemic Suppo Pandemic Suppo om Ca ee Lec u e s: Assessing S uden Sa is ac-
ion wi h P og am-Speci ic Assis ance
SA8 Unde s anding amids Connec i i y Is-
sues
Lec u e Unde s anding amids Connec i i y Issues: E alua ing S uden
Sa is ac ion in he Face o Technical Challenges
SA9 Vi ual Modali y T ea men E alua ion Vi ual Modali y T ea men E alua ion: Assessing S uden Sa is ac ion
wi h Changes in Lec u e In e ac ion and Suppo
2. SATISFACTION WITH INTERACTION IN THE VIRTUAL CLASSROOM
I1 In e ac ions in Online En i onmen s Vi ual Mode Colleague Communica ion: E alua ing S uden Sa is ac-
ion wi h In e ac ions in Online En i onmen s
I2 Communica ion and Doub Cla i ica ion Open Exp ession o Doub s in Vi ual Mode: Assessing S uden Sa is-
ac ion wi h Communica ion and Doub Cla i ica ion
I3 Flexibili y o Lec u e Demands Adap abili y Assessmen : Explo ing S uden Sa is ac ion wi h he Flex-
ibili y o Lec u e Demands
I4 Academic Mo i a ion S udy Mo i a ion Sa is ac ion: Assessing S uden Con en men wi h
Pe sonal Mo i a ional Le els in Academic Endea o s
I5 Modali y Lec u e Communica ion Vi ual Modali y Lec u e Communica ion: Assessing S uden Sa is ac-
ion wi h In e ac ion and Suppo in Online Lea ning
I6 Class Re lec ion Time Class Re lec ion Time Sa is ac ion: Assessing S uden Con en men
wi h Oppo uni ies o Con empla ion du ing Vi ual Lea ning
I7 Lec u e In e es in Heal h and Well-being Lec u e In e es in Heal h and Well-being: Assessing S uden Sa is ac-
ion wi h Facul y Conce ns o S uden Wel a e
I8 Class Du a ion Class Session Du a ion Sa is ac ion: Assessing S uden Con en men
wi h he Leng h o Vi ual Class Sessions
3. SATISFACTION WITH THE STUDY PROGRAM DEVELOPMENT
DS1 Online Lea ning Vi ual Modali y E alua ion Sa is ac ion: Assessing S uden Con en -
men wi h he Types o Assessmen s in Online Lea ning
DS2 Timelines in Online Lea ning Vi ual Mode Schedule Compliance: Assessing S uden Sa is ac ion
wi h Adhe ence o Timelines in Online Lea ning
DS3 Ease o Unde s anding Cou se Cla i y in Vi ual Lea ning: Assessing S uden Sa is ac ion wi h
he Ease o Unde s anding in Online Cou ses
DS4 Assessmen Va ie y Di e se E alua ion Me hods in Vi ual Lea ning: Assessing S uden Sa -
is ac ion wi h Assessmen Va ie y in Online Educa ion
480
Mansoo eh Kazemila i, Dalia S eimikiene
10.5709/ce.1897-9254.550DOI: CONTEMPORARY ECONOMICS
Vol. 18 Issue 4 475-4852024
should c ea e a dis ance ma ix o all s uden sa is ac-
ion i ems. This ma ix is composed o dis ances be-
ween e e y pai o i ems. The dis ance be ween i ems
depends only on he co ela ion coe icien , which
means i can be calcula ed easily and quickly. To ob ain
a dis ance based on co ela ion ρ
ij
, Man egna (1997)
p oposed he dis ance unc ion:
The dis ance ma ix D=(d
ij
) de ines he s uc u e o
a ne wo k ha consis s o 24 nodes, ep esen ing i ems.
This ne wo k is ully connec ed, undi ec ed, and weigh -
ed, wi h a o al o 276 connec ions be ween i s nodes.
An in iguing aspec eme ges when we examine a
dis ance ma ix de ined on a dioid. This ma ix nume i-
cally ep esen s a complex ne wo k, enabling us o add
and mul iply wo ne wo ks. Imagine a complex ne wo k
o n i ems as a connec ed, undi ec ed, weigh ed g aph
wi h n nodes. The weigh o he link be ween nodes a
and b quan i ies hei complex ela ionship, ac ing as a
dissimila i y o simila i y sco e be ween nodes a and b.
A comple e ne wo k can usually be depic ed g aphi-
cally, bu isualizing all connec ions would esul in a
clu e ed and di icul - o- ead image, especially o
small ne wo ks. The e o e, using an MST g aph is mo e
app op ia e in his con ex . Ne wo k analysis using MST
can e ec i ely simpli y he ep esen a ion o he s uc-
u es o 24 i ems based on D.
We iden i y he subdominan ul ame ic (SDU) o
D. The SDU es ablishes a axonomy among i ems, com-
monly ep esen ed as a dend og am. Then, we imple-
men he p ocedu e o iden i y he Fo es and an MST,
as sugges ed by Djauha i (2017), o ob ain he il e ed
ne wo k.
Le D
*
deno e he SDU o D, and ∆ be he adjacency
ma ix o he o es .
De ine D
2
=D × D, whe e mul iplica ion is de ined
con en ionally o elemen s in D. Addi ionally, de ine
ab=max{a,b} and a b=min{a,b} o all elemen s a
and b in D. I D
2
=D, hen D
*
=D
2
. O he wise, go o nex
s ep. Compu e D
4
=D
2
× D
2
. I D
4
=D
2
, hen D
*
=D
4
. O
else, compu e D
8
=D
4
×D
4
. The p ocess con inues un il
he - h i e a ion, whe e D
*
=D
2
. This p ocedu e needs
i e a ions whe e . I signi ies an ad ancemen in
compu a ional e iciency, speci ically enabling a p ede-
e mined numbe o i e a ions.
Once D
*
is de e mined, ∆ can be easily de i ed. Le
∆=D-D
*
(s anda d ma ix sub ac ion). The adjacency
ma ix ∆ is hen ob ained om D
*
by con e ing all ze o
o -diagonal elemen s o 1 and all non-ze o elemen s o
0.
To ind a Minimum Spanning T ee (MST), c e-
a e T
1
by o ming a sub-g aph o he o es a e e-
mo ing all i s lea es. I T
1
has no lea es, hen T
1
i sel
is conside ed an MST, and combining T
1
wi h all p e-
iously emo ed lea es esul s in an MST o D. I T
1
s ill con ains lea es, con inue emo ing lea es i e a-
i ely un il he k- h i e a ion, whe e T
k
has no lea es.
An MST o D is o med om T
k
wi h all lea es ha
we e p e iously emo ed.
Acco ding o his app oach and he esul s o e-
pea ing he abo e s eps wel e imes, he adjacency
ma ix shows ha he MST is unique, indica ing ha
he o es consis s o a single MST.
The MST is commonly employed o simpli y he
o iginal ne wo k and condense he mos impo an
in o ma ion. U ilizing Pajek so wa e, widely en-
do sed o ne wo k analysis (De Nooy e al., 2011;
Ba agelj & M a , 2003; Ba agelj & M a , 2004), al-
Table 1
Th ee Dimensions and Fac o s o S uden Sa is ac ion in Online Lea ning Du ing COVID-19 (Con inued)
3. SATISFACTION WITH THE STUDY PROGRAM DEVELOPMENT
DS5 Pandemic S udy P og am Pandemic S udy P og am Sa is ac ion: Assessing S uden Con en men
wi h Academic Expe iences Amids Challenging Times
DS6 Cou se Con en in Online Educa ion Con en Compliance in Vi ual Lea ning: E alua ing S uden Sa is ac-
ion wi h Adhe ence o Cou se Con en in Online Educa ion
DS7 Teaching App oaches Vi ual Modali y Lec u e Me hodology: Assessing S uden Sa is ac ion
wi h Teaching App oaches in Online Lea ning
www.ce. izja.pl
481
Topological Ne wo k Analysis and i s Applica ion on Re ealing Dimensions o S uden Sa is ac ion Unde he COVID-19 Pandemic
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License.
lows o g aphical isualiza ion o he simpli ied ne -
wo k. This isualiza ion helps in unde s anding he
complex ne wo k as a mo e s aigh o wa d s uc u e.
Once he simila i y measu e among ac o s is es-
ablished and he ne wo k is cons uc ed, he ocus
shi s o in e p e ing i s opology. Cen ali y mea-
su emen is a undamen al concep and one o he
mos ex ensi ely s udied heo ies in he ield o ne -
wo k analysis. Nume ous measu es ha e been de el-
oped o help in unde s anding he ne wo k by speci-
ying i s componen s and hei in e ela ionships.
They include deg ee, be weenness, closeness, eigen-
ec o cen ali ies, low be weenness, he ush index,
in o ma ion cen ali ies, he in luence measu es o
Ka z (1953), Hubbell (1965), Taylo s (1969) measu e
and Hoede (1978), e c. F eeman in (1979) p o ided
h ee basic measu es (deg ee, be weeness, closeness)
o answe he” wha is cen ali y” ques ion and o
which he p o ided canonical o mula ions. Bo ga i
(2005, 2006) explo ed obus ness o h ee cen ali y
measu es (deg ee, be weenness, closeness) in andom
g aphs.
Ne wo k cen ali y e e s o he posi ion o loca ion
o nodes wi hin a ne wo k. I is used o iden i y and
classi y impo an ac o s wi hin he ne wo k (Geis-
be ge e al., 2008; Xu e al., 2009; Espino and Hoyos,
2010; Abbasi & Al mann, 2011). Deg ee cen ali y,
be weenness cen ali y, and closeness cen ali y—key
me ics in ne wo k analysis—each p o ide unique
pe spec i es on he in e ac ions among i ems wi hin
he ne wo k. Gi en ha each cen ali y measu e
se es a speci ic ole in iden i ying in luen ial nodes,
hese h ee me ics will be u ilized in his esea ch.
4. Resul and Discussion4. Resul and Discussion
In his sec ion, we will use a g aphical ne wo k o
s uden sa is ac ion ac o s o highligh how dioid
algeb a can bene i ne wo k analysis.
Figu e 1 displays he co ela ion-based Mini-
mum Spanning T ee (MST) o he 24 ac o s ac oss
h ee dimensions o s uden sa is ac ion. This yields
a ne wo k ha is uncomple ed, weigh ed, and undi-
ec ed g aph. Each ac o is ep esen ed by i s sym-
bol and i is colo ed by i s dimension classi ica ion.
Once he MST is iden i ied, he ne wo k opology
i ep esen s is analyzed and summa ized nume ically
Figu e 1
Ne wo k Topology o 24 S uden Sa is ac ion Fac o s
482
Mansoo eh Kazemila i, Dalia S eimikiene
10.5709/ce.1897-9254.550DOI: CONTEMPORARY ECONOMICS
Vol. 18 Issue 4 475-4852024
using h ee widely used cen ali y measu es, which
cons i u es a me hod o sys em analysis. We assess
he ou comes de i ed om analyzing he ne wo k's
opology. The cha ac e is ics o dimensions a e classi-
ied in o 24 ac o s. In Table 2, he 24 ac o s a e clas-
si ied based on cen ali y measu es sco e.
Based on he deg ee cen ali y measu e, he num-
be o linkages anges om 1 o 3, wi h none exceed-
ing 3. The impo ance o ac o s is simila , and he e
is no signi ican ly dominan ac o . The subsequen
connec ed ac o s include h ee linkages, comp ising:
1. SA9 as Vi ual Modali y T ea men E alua ion
(blue node),
2. SA4 as Academic Adap a ion (blue node),
3. SA6 as Technological Facili a ion (blue node),
4. I8 as Class Session Du a ion Sa is ac ion
(g een node),
5. I3 as Flexibili y o Lec u e Demands, and
6. DS4 as Di e se E alua ion Me hods in Vi ual
Lea ning
Acco ding o he be weenness cen ali y measu e in
Table 2, SA9 (blue node) has he highes sco e (0.6) o
o he s ha show his ac o is he mos signi ican ac o
in he ollowing sense. The e o e, SA9 plays an impo -
an ole as a liaison ha could a ec he in o ma ion
among ac o s. The o he high sco ing ac o s a e SA4,
SA6 wi h highes sco e o be weenness and closeness
cen ali y.
Table 2
24 Fac o s and hei Cen ali y Measu es
No Node Deg ee Be weenness Closeness
1 SA1 2 0.087 0.209
2 SA2 1 0 0.174
3 SA3 2 0.498 0.245
4 SA4 3 0.549 0.25
5 SA5 1 0 0.202
6 SA6 3 0.533 0.235
7 SA7 2 0.443 0.213
8 SA8 2 0.474 0.23
9 SA9 3 0.601 0.255
10 I1 1 0 0.172
11 I2 1 0 0.151
12 I3 3 0.17 0.177
13 I4 2 0.166 0.198
14 I5 2 0.087 0.17
15 I6 1 0 0.151
16 I7 1 0 0.145
17 I8 3 0.312 0.205
18 DS1 2 0.403 0.195
19 DS2 2 0.166 0.155
20 DS3 2 0.087 0.153
21 DS4 3 0.379 0.177
22 DS5 1 0 0.134
23 DS6 2 0.087 0.137
24 DS7 1 0 0.121
