I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
AI
)
V
ol
.
14
, N
o.
2
,
A
pr
il
2025
, pp.
1663
~
1672
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
14
.i
2
.pp
1663
-
1672
1663
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
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s
c
or
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.c
om
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r
ap
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ase
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m
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t
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at
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ase
s:
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Wae
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j
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or
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e
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nt
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M
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n C
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o
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a
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s
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l
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l
qa
A
pp
l
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d U
ni
ve
r
s
i
t
y,
A
m
m
a
n, J
or
da
n
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
J
ul
29, 2024
R
e
vi
s
e
d
N
ov 3, 2024
A
c
c
e
pt
e
d
N
ov 14, 2024
There
has
been
an
increased
demand
for
structured
data
mining.
Gra
phs
are
among
the
most
extensively
researched
data
structures
in
d
iscrete
mathematics
and
computer
science.
Thus,
it
should
come
as
no
surpri
se
that
graph
-
based
data
mining
has
gained
popularity
in
rec
ent
years.
Graph
-
based
methods
for
a
transactio
n
database
are
necessa
ry
to
transform
all
the
information
into
a
graph
form
to
convenien
tly
extract
more
v
aluable
information
to
improve
the
decision
-
making
process.
Graph
-
base
d
data
min
ing
can
reve
al
and
measure
process
insights
in
a
detailed
str
uctural
compariso
n
strategy
that
is
ready
for
further
analysis
without
the
loss
of
significant
details.
This
paper
analyz
es
the
similarities
and
diffe
rences
among
four
of
the
most
popular
graph
-
based
methods
that
is
applied
t
o
mine
rules
from
transaction
databases
by
abstracting
them
out
as
a
concret
e
high
-
level inter
face a
nd connec
ting them into a
common spac
e.
K
e
y
w
o
r
d
s
:
D
a
ta
m
in
in
g
G
r
a
ph
R
ul
e
m
in
in
g
S
tr
uc
tu
r
e
d da
ta
T
r
a
ns
a
c
ti
on da
t
a
ba
s
e
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
W
a
e
l
A
hm
a
d A
lZ
oubi
D
e
pa
r
tm
e
nt
of
A
ppl
ie
d S
c
ie
nc
e
s
, A
jl
oun Unive
r
s
it
y C
ol
le
g
e
, A
l
-
B
a
lq
a
A
ppl
ie
d U
ni
ve
r
s
it
y
A
jl
oun 26816, J
or
da
n
E
m
a
il
:
w
a
2010
@
ba
u.e
du.j
o
1.
I
N
T
R
O
D
U
C
T
I
O
N
G
r
a
ph
-
ba
s
e
d
m
e
th
ods
f
or
a
tr
a
ns
a
c
ti
on
da
ta
ba
s
e
a
r
e
ne
c
e
s
s
a
r
y
t
o
tr
a
ns
f
or
m
a
ll
th
e
in
f
or
m
a
ti
on
in
to
a
gr
a
ph
f
or
m
to
c
onve
ni
e
nt
ly
e
xt
r
a
c
t
m
or
e
va
lu
a
bl
e
in
f
or
m
a
ti
on
[
1]
–
[
3
]
.
G
r
a
ph
-
ba
s
e
d
da
ta
m
in
in
g
c
a
n
r
e
ve
a
l
a
nd
m
e
a
s
ur
e
pr
oc
e
s
s
in
s
ig
ht
s
in
a
de
ta
il
e
d
s
tr
uc
tu
r
a
l
c
om
pa
r
is
on
s
tr
a
te
gy
th
a
t
i
s
r
e
a
dy
f
or
f
ur
th
e
r
a
na
ly
s
is
w
it
hout
th
e
lo
s
s
of
s
ig
ni
f
ic
a
nt
de
ta
il
s
[
4]
.
I
n
a
ddi
ti
on,
th
e
gr
a
p
h
-
ba
s
e
d
m
e
th
ods
pr
oc
e
s
s
c
a
n
be
c
ons
id
e
r
e
d
a
s
a
pr
oc
e
s
s
m
in
in
g m
e
th
od.
T
h
is
r
e
s
e
a
r
c
h a
im
s
t
o s
y
s
te
m
a
t
ic
a
l
ly
und
e
r
s
t
a
n
d
t
he
tr
a
d
e
-
of
f
s
a
m
ong
gr
a
p
h
-
b
a
s
e
d
m
e
t
hod
s
f
or
m
in
in
g
tr
a
n
s
a
c
ti
on
d
a
t
a
s
e
ts
by
c
om
pa
r
in
g t
h
e
m
.
T
he
r
e
a
r
e
f
our
m
a
i
n
m
e
t
hod
s
t
o m
in
e
tr
a
n
s
a
c
ti
on
d
a
t
a
s
e
ts
u
s
in
g gr
a
ph
s
,
th
e
y
a
r
e
:
c
li
q
ue
pe
r
c
o
la
ti
o
n
s
ys
te
m
[
5]
,
a
dj
a
c
e
nc
y
m
a
tr
ix
[
6
]
,
g
r
a
p
h
ne
ur
a
l
ne
tw
or
k
(
G
N
N
)
[
7]
a
n
d
n
e
tw
or
k
-
ba
s
e
d
v
is
u
a
li
z
a
ti
o
n
[
8]
.
E
a
c
h
on
e
of
th
e
s
e
m
e
th
o
d
s
f
ol
lo
w
th
e
s
a
m
e
g
e
n
e
r
a
l
id
e
a
:
c
on
s
tr
u
c
ti
ng
a
gr
a
p
h
th
a
t
c
a
pt
ur
e
s
t
he
r
e
la
t
io
ns
b
e
tw
e
e
n
di
f
f
e
r
e
nt
pa
r
t
s
of
th
e
s
tr
u
c
t
ur
e
d
da
t
a
.
D
e
s
pi
t
e
th
e
di
ve
r
s
it
y
of
m
e
t
ho
ds
a
nd
t
he
va
r
i
a
t
io
n
s
i
n
t
h
e
e
xa
c
t
f
or
m
t
h
a
t
t
h
e
f
in
a
l
t
a
s
k
-
r
e
l
a
te
d
gr
a
ph
t
a
k
e
s
,
s
om
e
c
l
e
a
r
o
r
g
a
ni
z
i
ng
pr
i
nc
ip
l
e
s
e
m
e
r
g
e
.
A
tr
a
ns
a
c
ti
on
da
t
a
ba
s
e
is
a
c
ol
le
c
ti
on
of
r
e
c
or
ds
;
e
a
c
h
r
e
c
or
d
c
ont
a
in
s
pi
e
c
e
s
of
da
ta
.
T
h
e
s
e
r
e
c
or
ds
a
r
e
a
ls
o
c
a
ll
e
d
tr
a
n
s
a
c
ti
ons
.
A
gr
a
ph
d
a
ta
ba
s
e
is
a
d
a
ta
ba
s
e
m
a
na
ge
m
e
nt
s
y
s
te
m
th
a
t
us
e
s
gr
a
ph
s
tr
uc
tu
r
e
s
to
s
to
r
e
,
m
a
p
a
nd
que
r
y
r
e
la
ti
ons
hi
p
s
.
E
ve
r
y
e
le
m
e
nt
c
ont
a
in
s
a
di
r
e
c
t
poi
nt
e
r
to
it
s
a
dj
a
c
e
nt
e
le
m
e
nt
a
nd
c
a
n
a
ls
o
be
us
e
d
to
pe
r
f
or
m
s
e
a
r
c
h
in
c
ons
ta
nt
ti
m
e
us
in
g
ha
s
h
in
d
e
x
[
9]
.
T
he
tr
a
ns
a
c
ti
on
da
ta
ba
s
e
m
a
na
ge
m
e
nt
s
ys
te
m
s
uppor
ts
tr
a
ns
a
c
ti
ons
f
r
om
m
ul
ti
pl
e
c
us
to
m
e
r
s
a
nd
d
oe
s
not
c
ont
a
in
a
ny
c
us
to
m
e
r
m
a
s
te
r
da
ta
.
A
tr
a
ns
a
c
ti
on
da
ta
ba
s
e
doe
s
not
a
ll
ow
f
or
th
e
f
ul
l
c
a
pa
bi
li
ti
e
s
of
a
tr
a
ns
a
c
ti
on
to
be
r
e
pr
e
s
e
nt
e
d.
I
t
a
bs
tr
a
c
ts
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
2025
:
1663
-
1672
1664
tr
a
ns
a
c
ti
ons
to
a
f
or
m
th
a
t
is
c
om
pa
ti
bl
e
w
it
h
th
e
m
a
c
hi
n
e
r
y
of
th
e
tr
a
ns
a
c
ti
on
da
ta
ba
s
e
.
A
gr
a
ph
da
ta
ba
s
e
a
tt
e
m
pt
s
t
o c
a
pt
ur
e
t
he
f
ul
l
de
ta
il
of
a
t
r
a
ns
a
c
ti
on
[
10]
.
W
e
out
li
ne
d
a
c
om
pa
r
a
ti
ve
s
tu
dy
on
th
e
gr
a
ph
-
ba
s
e
d
a
ppr
oa
c
he
s
f
or
m
in
in
g
di
f
f
e
r
e
nt
us
e
f
ul
pa
tt
e
r
ns
by
gr
ow
in
g
a
lg
or
it
h
m
s
in
c
a
s
e
of
th
e
tr
a
ns
a
c
ti
on
da
ta
ba
s
e
[
11]
.
T
a
bl
e
1
br
ie
f
ly
e
xpl
a
in
s
s
om
e
of
th
e
m
a
in
c
ha
r
a
c
te
r
is
ti
c
s
of
th
e
s
e
m
e
th
ods
.
T
hi
s
ta
bl
e
he
lp
s
to
f
oc
us
th
e
di
f
f
e
r
e
nt
f
e
a
tu
r
e
s
a
nd
a
ppl
ic
a
ti
ons
of
e
a
c
h
m
e
th
od f
or
ne
twor
k a
na
ly
s
is
a
nd vis
ua
li
z
a
ti
on.
T
a
bl
e
1. G
r
a
ph
-
ba
s
e
d m
in
in
g m
e
th
ods
'
c
ha
r
a
c
te
r
is
ti
c
s
M
e
t
hod
D
e
s
c
r
i
pt
i
on
U
s
e
s
G
r
a
ph
r
e
pr
e
s
e
nt
a
t
i
on
I
nt
e
r
a
c
t
i
vi
t
y
1.
C
l
i
que
pe
r
c
ol
a
t
i
on
s
ys
t
e
m
S
ys
t
e
m
us
e
d
t
o
f
i
nd
a
nd
a
na
l
yz
e
c
om
pl
e
t
e
s
ub
gr
a
phs
(
c
l
i
que
s
)
i
n
ne
t
w
or
ks
,
f
oc
us
i
ng
on
i
de
nt
i
f
yi
ng
f
ul
l
y
c
onne
c
t
e
d
gr
oups
of
node
s
.
I
de
nt
i
f
yi
ng
i
nt
e
r
c
onne
c
t
e
d
gr
oups
a
nd
c
om
m
uni
t
i
e
s
w
i
t
hi
n ne
t
w
or
ks
.
F
oc
us
e
s
on
i
de
nt
i
f
yi
ng
c
l
i
que
s
,
not
a
di
r
e
c
t
vi
s
ua
l
r
e
pr
e
s
e
nt
a
t
i
on.
M
i
ni
m
a
l
i
nt
e
r
a
c
t
i
on:
m
a
nua
l
l
y
i
ns
pe
c
t
i
ng
i
de
nt
i
f
i
e
d
c
l
i
que
s
i
s
f
r
e
que
nt
l
y ne
c
e
s
s
a
r
y.
2.
A
dj
a
c
e
nc
y
m
a
t
r
i
x
T
hi
s
m
e
t
hod
r
e
pr
e
s
e
nt
s
t
he
r
e
l
a
t
i
ons
hi
ps
a
m
ong
t
he
node
s
i
n
2
D
a
r
r
a
y
(
m
a
t
r
i
x)
s
how
i
ng
c
onne
c
t
i
ons
a
s
bi
n
a
r
y
va
l
ue
s
(
pr
e
s
e
nc
e
or
a
bs
e
nc
e
of
e
dge
s
)
.
S
t
udy
i
n
g
n
e
t
w
o
r
k
c
ons
t
r
uc
t
i
o
n
a
c
c
u
r
a
t
e
l
y,
c
om
put
i
n
g
n
e
t
w
o
r
k
m
e
t
r
i
c
s
l
i
ke
d
e
g
r
e
e
s
a
nd s
ho
r
t
e
s
t
r
ou
t
e
s
.
R
e
pr
e
s
e
nt
s
c
onne
c
t
i
ons
be
t
w
e
e
n
node
s
i
n
a
m
a
t
r
i
x
f
or
m
.
S
t
a
t
i
c
r
e
pr
e
s
e
nt
a
t
i
on,
ne
e
ds
m
a
nua
l
a
dj
us
t
m
e
nt
f
or
ne
t
w
or
k c
ha
nge
s
.
3.
GNN
m
e
t
hod
N
e
ur
a
l
ne
t
w
or
k
a
ppr
oa
c
h
t
o
l
e
a
r
n
node
a
nd
e
dge
f
e
a
t
ur
e
s
f
or
pr
e
di
c
t
i
on
a
nd
c
l
a
s
s
i
f
i
c
a
t
i
on
t
a
s
ks
i
n ne
t
w
or
ks
.
N
ode
c
l
a
s
s
i
f
i
c
a
t
i
on,
l
i
nk
pr
e
di
c
t
i
on,
a
nd
c
om
m
uni
t
y
de
t
e
c
t
i
on
i
n c
om
pl
e
x ne
t
w
or
ks
.
L
e
a
r
ns
node
a
nd
e
dge
f
e
a
t
ur
e
s
us
i
ng
de
e
p
l
e
a
r
ni
ng t
e
c
hni
que
s
.
I
nt
e
r
a
c
t
i
ve
f
or
ne
t
w
or
k
e
xpl
or
a
t
i
on
a
nd
pr
e
di
c
t
i
ve
t
a
s
ks
.
4.
N
e
t
w
or
k
-
ba
s
e
d
v
i
s
ua
l
i
z
a
t
i
on
V
i
s
ua
l
r
e
pr
e
s
e
nt
a
t
i
on
t
e
c
hni
que
f
or
ne
t
w
or
ks
,
s
how
i
ng
node
s
a
nd
l
i
nks
i
n
a
g
r
a
phi
c
a
l
a
nd
i
nt
e
r
a
c
t
i
ve
m
a
nne
r
.
V
i
s
ua
l
e
xpl
or
a
t
i
on
of
ne
t
w
or
k
s
t
r
uc
t
ur
e
s
,
unde
r
s
t
a
ndi
ng
r
e
l
a
t
i
ons
hi
ps
a
nd
i
de
nt
i
f
yi
ng pa
t
t
e
r
ns
.
P
r
ovi
de
s
vi
s
ua
l
i
ns
i
ght
s
i
nt
o
ne
t
w
or
k
t
opol
ogy
a
nd
dyna
m
i
c
s
.
H
i
ghl
y
i
nt
e
r
a
c
t
i
ve
,
a
l
l
ow
s
r
e
a
l
-
t
i
m
e
e
xpl
or
a
t
i
on
a
nd
a
na
l
ys
i
s
.
T
hi
s
s
tu
dy
c
ove
r
s
gr
a
ph
-
ba
s
e
d
a
lg
or
it
hm
s
f
or
da
ta
a
na
ly
s
is
of
tr
a
ns
a
c
ti
on
da
ta
ba
s
e
s
a
nd
pr
ovi
de
s
a
c
om
pa
r
a
ti
ve
a
na
ly
s
i
s
r
e
ga
r
di
ng
s
e
le
c
te
d
pr
ope
r
ty
de
s
c
r
ip
to
r
s
.
R
e
ta
il
da
ta
s
e
ts
of
1000
tr
a
ns
a
c
ti
on
s
w
il
l
be
ta
ke
n
a
s
a
c
a
s
e
s
tu
dy
to
c
la
r
if
y
th
e
r
ol
e
of
e
a
c
h
m
e
th
od
in
e
xt
r
a
c
ti
ng
th
e
de
s
ir
e
d
a
s
s
oc
ia
ti
on
r
ul
e
s
,
c
om
pa
r
e
a
m
ong
th
e
m
a
nd
s
o
e
nha
nc
e
th
e
de
c
i
s
io
n
-
m
a
ki
ng
pr
oc
e
s
s
.
T
o
th
e
be
s
t
of
our
knowle
dge
,
w
e
in
tr
oduc
e
a
c
om
pa
r
a
ti
ve
s
tu
dy of
t
he
gr
a
ph
-
ba
s
e
d m
e
th
ods
u
s
e
d t
o di
s
c
ove
r
r
ul
e
s
f
r
om
t
r
a
ns
a
c
ti
on da
ta
s
e
ts
.
T
he
ov
e
r
a
ll
s
tr
u
c
tu
r
e
of
th
e
r
e
s
e
a
r
c
h
is
or
g
a
ni
z
e
d
a
s
f
ol
lo
w
s
.
S
e
c
ti
on
2
ta
lk
s
a
bo
ut
th
e
m
a
in
gr
a
p
h
-
ba
s
e
d m
e
th
od
s
f
or
t
r
a
n
s
a
c
ti
on d
a
ta
s
e
ts
.
S
c
ti
o
n 3
e
xpl
a
in
s
br
ie
f
ly
t
he
r
e
s
e
a
r
c
h
m
e
th
odol
o
gy. S
e
c
ti
o
n 4 di
s
c
us
s
e
s
th
e
c
om
p
a
r
a
ti
ve
a
n
a
ly
s
i
s
of
th
e
s
e
m
e
t
hod
s
.
S
e
c
ti
on
5
th
e
r
e
s
u
lt
s
of
pr
e
vi
o
us
s
tu
di
e
s
w
e
r
e
c
om
pr
e
he
n
s
iv
e
ly
r
e
vi
e
w
e
d
a
nd
a
na
l
yz
e
d u
s
in
g
th
e
c
r
it
e
r
i
a
d
e
s
c
r
ib
e
d
t
he
r
e
. L
a
s
tl
y
,
s
e
c
ti
on
6 c
onc
lu
de
s
t
hi
s
p
a
pe
r
.
2.
G
R
A
P
H
B
A
S
E
D
M
E
T
H
O
D
S
F
O
R
T
R
A
N
S
A
C
T
I
O
N
D
A
T
A
S
E
T
S
A
s
w
e
m
e
n
ti
o
ne
d e
a
r
li
e
r
i
n
t
h
e
i
nt
r
o
du
c
ti
on
, a
d
a
t
a
s
e
t
of
r
e
ta
il
s
a
le
s
w
il
l
b
e
s
t
udi
e
d
a
nd a
na
l
y
z
e
d s
in
c
e
th
i
s
ty
pe
of
da
t
a
s
e
t
s
ha
s
b
e
e
n
d
e
v
e
l
op
e
d
s
a
f
e
l
y
w
it
h
th
e
c
om
i
n
g
of
pr
e
s
id
e
nt
d
a
t
a
s
c
i
e
n
c
e
m
e
th
o
d
s
a
n
d
to
ol
s
[
12]
.
N
o
w
a
da
y
s
,
r
e
ta
il
e
nt
e
r
pr
is
e
s
c
r
e
a
t
e
a
d
v
a
n
c
e
d
te
c
h
ni
q
u
e
s
t
o
de
r
iv
e
m
e
a
n
in
gf
ul
c
o
nc
l
u
s
io
n
s
f
r
om
m
a
s
s
iv
e
vol
u
m
e
s
of
tr
a
n
s
a
c
ti
on
a
l
d
a
ta
[
1
3]
.
T
he
m
o
s
t
c
om
m
on
a
m
on
g
th
e
s
e
t
e
c
hni
qu
e
s
a
r
e
:
t
he
c
li
q
ue
p
e
r
c
ol
a
ti
on
s
y
s
t
e
m
,
a
dj
a
c
e
nc
y
m
a
tr
i
x
a
n
a
ly
s
is
,
G
N
N
s
,
a
n
d
n
e
t
w
or
k
-
b
a
s
e
d
vi
s
u
a
li
z
a
ti
o
n
.
T
he
s
e
a
l
gor
i
th
m
s
of
f
e
r
p
ow
e
r
f
u
l
w
a
ys
to
u
nc
ov
e
r
hi
d
de
n
p
a
t
te
r
n
s
,
c
o
m
pl
e
x
r
e
la
ti
o
n
s
hi
p
s
b
e
t
w
e
e
n
pr
o
du
c
t
s
a
n
d
c
u
s
t
om
e
r
s
w
il
l
b
e
d
is
c
o
ve
r
e
d,
a
nd
t
ot
a
ll
y
im
pr
o
ve
d
e
c
i
s
io
n
-
m
a
ki
ng.
W
e
w
i
ll
e
x
a
m
in
e
h
ow
th
e
s
e
t
e
c
hn
iq
u
e
s
c
a
n
be
s
u
c
c
e
s
s
f
ul
ly
u
s
e
d
i
n
r
e
t
a
il
s
a
le
s
e
nv
ir
o
nm
e
nt
s
to
e
nh
a
n
c
e
c
on
s
um
e
r
e
ng
a
g
e
m
e
n
t,
op
ti
m
iz
e
s
t
r
a
t
e
g
ie
s
,
a
n
d
s
pur
b
us
in
e
s
s
gr
o
w
th
.
R
e
t
a
il
c
om
pa
ni
e
s
c
a
n
i
m
pr
o
ve
c
u
s
to
m
e
r
s
a
ti
s
f
a
c
t
io
n
,
b
oo
s
t
o
pe
r
a
t
io
na
l
e
f
f
i
c
i
e
n
c
y
,
a
nd
i
m
pr
o
ve
th
e
ir
m
a
r
k
e
t
in
g
s
tr
a
t
e
g
y
by
in
c
or
por
a
ti
ng
th
e
s
e
t
a
c
ti
c
s
a
nd
a
n
a
l
yz
in
g
th
e
li
nk
s
a
nd
tr
e
nd
s
i
n
t
he
ir
s
a
l
e
s
d
a
t
a
.
I
n
t
he
f
ol
l
ow
in
g
s
u
b
-
s
e
c
ti
on
s
,
w
e
w
il
l
de
s
c
r
ib
e
br
i
e
f
l
y
how
t
he
s
e
t
e
c
hn
iq
ue
s
a
r
e
u
s
e
d
in
th
e
c
o
nt
e
xt
of
r
e
t
a
i
l
s
a
l
e
s
d
a
t
a
s
e
t
.
2.1.
C
li
q
u
e
p
e
r
c
ol
at
io
n
m
e
t
h
od
T
he
c
li
que
pe
r
c
ol
a
ti
on me
th
od i
s
a
c
om
m
on me
th
od f
or
e
xa
m
in
in
g t
he
ove
r
ly
in
g publi
c
c
ons
tr
uc
ti
o
n
of
ne
twor
ks
.
T
he
c
li
que
p
e
r
c
ol
a
ti
on
s
y
s
te
m
c
a
n
be
u
s
e
d
in
r
e
ta
il
s
a
le
s
to
f
in
d
pr
oduc
ts
or
c
a
te
gor
y
c
lu
s
te
r
s
th
a
t
a
r
e
c
om
m
onl
y
pur
c
ha
s
e
d
to
ge
th
e
r
,
a
s
w
e
ll
a
s
s
ig
ni
f
ic
a
nt
c
or
r
e
la
ti
ons
be
twe
e
n
th
e
m
.
F
or
in
s
ta
nc
e
,
it
c
a
n
r
e
ve
a
l
pr
oduc
t
gr
oups
t
ha
t
a
r
e
f
r
e
que
nt
ly
pur
c
ha
s
e
d t
oge
th
e
r
or
c
lo
s
e
c
onne
c
ti
ons
be
twe
e
n
c
a
te
gor
ie
s
.
2.2.
A
d
j
ac
e
n
c
y m
at
r
ix
T
h
e
a
d
ja
c
e
n
c
y
m
a
tr
ix
of
f
e
r
s
a
m
a
tr
ix
r
e
pr
e
s
e
n
ta
t
io
n
of
no
de
s
a
n
d
th
e
ir
pa
ir
w
is
e
r
e
l
a
t
io
n
s
hi
p
s
ba
s
e
d on
tr
a
n
s
a
c
ti
on
in
t
e
r
a
c
ti
o
n
s
s
h
ow
i
ng
c
on
ne
c
ti
on
s
a
s
bi
na
r
y
v
a
l
ue
s
(
e
xi
s
te
nc
e
or
non
e
x
i
s
t
e
n
c
e
of
e
dg
e
s
)
.
I
n
r
e
t
a
i
l
Evaluation Warning : The document was created with Spire.PDF for Python.
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on databas
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s
:
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par
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(
W
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1665
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it
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s
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pr
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te
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a
c
h
r
ow
a
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u
m
n,
a
nd
t
he
m
a
tr
i
x
s
ho
w
s
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h
e
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th
e
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la
ti
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hi
p
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t
w
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e
n
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o
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n
ot
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s
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t
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s
m
a
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to
l
o
ok
a
t
r
e
la
ti
o
n
s
hi
p
s
a
nd
f
in
d
f
r
e
s
h p
a
t
te
r
n
s
i
n
s
a
le
s
d
a
t
a
.
2.3.
G
r
ap
h
n
e
u
r
al
n
e
t
w
or
k
I
n
di
s
c
ove
r
y
of
c
om
pl
e
x
a
s
s
oc
i
a
ti
ons
f
r
om
tr
a
ns
a
c
ti
on
da
ta
,
t
he
G
N
N
s
pl
a
y
a
n
im
por
ta
nt
r
ol
e
in
f
in
di
ng
hi
dde
n
r
ul
e
s
th
a
t
r
e
pr
e
s
e
nt
th
e
r
e
la
ti
ons
a
m
ong
pr
oduc
ts
.
G
N
N
s
s
ig
ni
f
y
th
e
tr
a
ns
a
c
ti
ons
a
s
gr
a
ph
s
to
f
or
e
c
a
s
t
c
onc
lu
s
io
ns
s
u
c
h
a
s
c
us
to
m
e
r
c
om
por
tm
e
nt
,
pr
oduc
t
c
om
m
e
nda
ti
ons
,
or
de
c
e
it
f
ul
a
c
ti
vi
ty
.
G
N
N
a
lg
or
it
hm
s
a
r
e
us
e
d t
o a
s
s
e
s
s
r
e
ta
il
s
a
l
e
s
da
ta
a
nd a
nt
ic
ip
a
te
buye
r
be
ha
vi
or
by me
a
ns
of
pr
oduc
t
r
e
la
ti
ons
hi
ps
a
nd
pr
io
r
pur
c
ha
s
e
pa
tt
e
r
ns
.
G
N
N
s
a
r
e
us
e
f
ul
f
or
unde
r
s
ta
ndi
ng
c
om
pl
ic
a
te
d
li
nka
ge
s
be
twe
e
n
goods
a
nd
c
ons
um
e
r
s
a
s
w
e
ll
a
s
e
xa
m
in
in
g how ma
r
ke
ti
ng a
nd pr
om
ot
io
ns
a
f
f
e
c
t
th
e
s
e
c
onn
e
c
ti
ons
.
2.4.
N
e
t
w
or
k
-
b
as
e
d
vi
s
u
al
iz
at
io
n
T
hi
s
m
e
th
od
gi
ve
s
gr
a
phi
c
a
l
de
pi
c
ti
on
f
or
ne
twor
ks
,
di
s
pl
a
yi
n
g
node
s
a
nd
e
dge
s
in
a
gr
a
phi
c
a
l
a
nd
c
ol
la
bor
a
ti
ve
w
a
y.
V
is
u
a
l
r
e
pr
e
s
e
nt
a
ti
on
a
nd
a
na
ly
s
i
s
of
th
e
out
c
om
e
s
of
th
e
G
N
N
,
a
dj
a
c
e
nc
y
m
a
tr
ix
,
a
nd
c
li
que
pe
r
c
ol
a
ti
on
s
ys
t
e
m
pr
e
di
c
ti
ons
in
r
e
ta
il
s
a
le
s
d
a
ta
a
r
e
done
by
ne
twor
k
-
ba
s
e
d
vi
s
u
a
li
z
a
ti
on.
I
t
he
lp
s
a
na
ly
s
ts
a
nd
m
a
n
a
ge
r
s
m
a
k
e
ba
s
e
d
on
da
ta
s
tr
a
te
gi
c
d
e
c
is
io
ns
by
of
f
e
r
in
g
a
n
il
lu
s
tr
a
ti
on
of
th
e
c
om
pl
e
x
r
e
la
ti
ons
hi
ps
a
m
ong pr
oduc
ts
.
3.
R
E
S
E
A
R
C
H
M
E
T
H
O
D
O
L
O
G
Y
T
he
s
a
m
e
s
e
t
of
da
t
a
a
c
r
os
s
a
ll
te
s
t
e
d
m
e
th
ods
i
s
us
e
d
dur
in
g
t
he
c
om
pa
r
a
ti
ve
s
tu
dy.
T
hi
s
a
ppr
oa
c
h
e
ns
ur
e
s
f
a
ir
ne
s
s
a
nd
c
ons
is
t
e
nc
y
in
e
va
lu
a
ti
ng
th
e
pe
r
f
or
m
a
nc
e
of
di
f
f
e
r
e
nt
gr
a
ph
-
ba
s
e
d
m
e
th
ods
f
or
m
in
in
g
tr
a
ns
a
c
ti
on
da
ta
s
e
t
s
[
14]
.
T
he
m
a
in
gr
a
ph
-
ba
s
e
d
m
e
th
ods
to
m
in
e
r
ul
e
s
f
r
om
tr
a
ns
a
c
ti
on
da
ta
s
e
ts
,
i.
e
.,
c
li
que
pe
r
c
ol
a
ti
on,
a
dj
a
c
e
nc
y
m
a
tr
ix
,
G
N
N
a
nd
gr
a
ph
vi
s
ua
li
z
a
ti
on
a
r
e
te
s
te
d
ove
r
th
e
s
a
m
e
s
e
t
of
tr
a
ns
a
c
ti
ons
.
A
n
in
tu
it
iv
e
c
hoi
c
e
is
to
us
e
a
gr
a
ph
da
ta
ba
s
e
a
s
a
ne
w
ty
pe
of
da
ta
ba
s
e
a
nd
th
us
th
is
te
c
hnol
ogy
ha
s
ge
ne
r
a
te
d
gr
e
a
t
a
tt
e
nt
io
n.
T
he
r
e
a
r
e
s
e
ve
r
a
l
s
ur
ve
y
s
in
th
e
li
te
r
a
tu
r
e
th
a
t
s
um
m
a
r
iz
e
th
e
e
xi
s
ti
ng
gr
a
ph
da
ta
ba
s
e
s
a
nd
th
e
ir
a
ppl
ic
a
ti
ons
[
15]
.
A
c
om
pa
r
a
ti
ve
s
tu
dy f
oc
us
in
g on gr
a
ph
-
ba
s
e
d m
e
th
od
s
us
e
d f
or
m
in
in
g t
r
a
ns
a
c
ti
on da
ta
s
e
ts
i
nvol
ve
s
e
va
lu
a
ti
ng
va
r
io
us
t
e
c
hni
que
s
w
it
hi
n
th
is
dom
a
in
w
il
l
be
di
s
c
us
s
e
d.
F
ig
ur
e
1
hi
ghl
ig
ht
s
th
e
m
a
in
s
te
ps
to
di
s
c
ove
r
th
e
f
in
d
out
th
e
be
s
t
c
hoi
c
e
by
do
a
n
e
f
f
ic
ie
nt
c
o
m
pa
r
is
on
a
m
ong
gr
a
ph
-
ba
s
e
d
m
e
th
ods
f
r
om
c
us
to
m
e
r
da
ta
.
T
he
s
e
s
te
p
s
im
pr
ove
th
e
a
c
c
ur
a
c
y
a
nd
tr
ut
h
of
th
e
c
om
pa
r
a
ti
ve
s
tu
dy'
s
r
e
s
ul
ts
,
th
i
s
w
il
l
le
a
d
to
w
or
th
y
r
e
m
a
r
ks
in
to
th
e
be
s
t
m
e
th
od(
s
)
f
or
e
xt
r
a
c
ti
ng
de
s
ir
e
d
r
ul
e
s
f
r
om
tr
a
ns
a
c
ti
on
da
ta
s
e
ts
.
T
h
e
f
ol
lo
w
in
g
s
ubs
e
c
ti
on
s
t
a
lk
s
br
ie
f
ly
a
bout
e
a
c
h on
e
of
t
he
s
e
s
t
e
ps
.
F
ig
ur
e
1. T
he
f
lo
w
c
ha
r
t
of
t
he
e
xpe
r
im
e
nt
a
l
m
e
th
ods
a
ppl
ie
d
3.1.
D
at
as
e
t
s
e
le
c
t
io
n
C
hoos
in
g
th
e
r
ig
ht
da
ta
s
e
t
is
not
a
s
s
im
pl
e
a
s
m
a
ny
pe
opl
e
th
in
k,
a
s
th
e
r
e
a
r
e
c
r
it
e
r
ia
f
or
c
hoos
in
g
th
e
a
ppr
opr
ia
te
da
ta
s
e
t,
s
uc
h
a
s
b
e
in
g
c
om
pa
ti
bl
e
w
it
h
th
e
f
ie
ld
of
in
te
r
e
s
t
or
s
tu
dy,
a
nd
it
m
us
t
a
f
f
or
d
Y
e
s
S
t
a
rt
Choos
e
t
he
da
t
a
s
e
t
Cl
e
a
n
t
he
da
t
a
s
e
t
Is
da
t
a
s
e
t
uni
form
?
D
a
t
a
s
e
t
a
na
l
ys
i
s
A
ppl
y
m
e
t
hods
D
o
c
om
pa
ri
s
on
Re
s
ul
t
s
E
n
d
No
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
2025
:
1663
-
1672
1666
a
de
qua
te
tr
a
ns
a
c
ti
ona
l
da
ta
.
T
he
c
hos
e
n
da
ta
s
e
t
s
houl
d
a
ls
o
b
e
c
om
pl
e
te
,
a
c
c
ur
a
te
a
nd
f
r
e
e
of
out
li
e
r
s
.
T
he
s
a
m
e
s
e
t
of
da
ta
w
il
l
be
u
s
e
d
f
or
e
a
c
h
m
e
th
od
und
e
r
in
ve
s
ti
ga
ti
on
dur
in
g
th
e
c
om
pa
r
is
on
a
na
ly
s
i
s
.
T
hi
s
m
e
th
odol
ogy
gua
r
a
nt
e
e
s
im
pa
r
ti
a
li
ty
a
nd
uni
f
or
m
it
y
w
hi
le
a
s
s
e
s
s
in
g
th
e
e
f
f
ic
a
c
y
of
va
r
io
us
gr
a
ph
-
ba
s
e
d
te
c
hni
que
s
f
or
t
r
a
ns
a
c
ti
on da
ta
s
e
t
m
in
in
g.
3.2.
D
at
as
e
t
c
le
an
in
g an
d
p
r
e
p
r
oc
e
s
s
in
g
D
a
ta
c
le
a
ni
ng
is
a
n
im
por
ta
nt
s
te
p
in
im
pr
ovi
ng
th
e
s
upe
r
io
r
it
y
of
th
e
da
ta
a
nd
c
onf
ir
m
th
a
t
w
e
c
a
n
in
f
e
r
e
lo
que
nt
r
ul
e
s
.
T
o
gua
r
a
nt
e
e
c
ons
i
s
te
nc
y
a
nd
qua
li
ty
o
f
da
ta
,
c
le
a
n
up
a
nd
pr
e
pr
oc
e
s
s
th
e
da
ta
s
e
t.
D
e
pe
ndi
ng
on
th
e
r
e
qui
r
e
m
e
nt
s
of
e
a
c
h
a
ppr
oa
c
h,
th
i
s
s
t
a
ge
m
a
y
in
vol
ve
r
e
s
ol
vi
ng
m
i
s
s
in
g
v
a
lu
e
s
,
nor
m
a
li
z
in
g da
ta
, a
nd e
nc
odi
ng c
a
te
gor
ic
a
l
v
a
r
ia
bl
e
s
.
3.3.
A
p
p
ly
m
e
t
h
od
s
on
u
n
if
or
m
d
at
as
e
t
W
he
n
th
e
s
e
le
c
te
d
da
ta
s
e
t
is
r
e
a
dy
to
be
u
s
e
d,
i.
e
.
it
is
c
le
a
ne
d
f
r
om
a
ny
out
li
e
r
s
or
m
is
s
in
g
va
lu
e
s
,
th
e
gr
a
ph
-
ba
s
e
d
m
e
th
ods
w
il
l
be
us
e
d
di
r
e
c
tl
y
to
a
s
s
is
t
in
m
a
ki
ng
r
ig
ht
de
c
is
io
ns
a
nd
th
e
ove
r
a
ll
m
in
in
g
pr
oc
e
s
s
w
il
l
b
e
im
pr
ove
d.
U
ti
li
z
e
th
e
s
ta
nd
a
r
di
z
e
d
da
ta
s
e
t
w
it
h
e
ve
r
y
gr
a
ph
-
ba
s
e
d
te
c
hni
que
,
f
ol
lo
w
in
g
th
e
s
a
m
e
gui
de
li
ne
s
.
T
o
e
n
s
ur
e
c
om
pa
r
a
bi
li
ty
a
nd
r
e
m
ove
bi
a
s
,
a
ll
m
e
th
ods
m
us
t
us
e
th
e
s
a
m
e
pr
e
pr
oc
e
s
s
in
g
pr
oc
e
dur
e
s
a
nd s
e
tt
in
g
s
.
3.4.
A
n
al
ys
is
an
d
e
val
u
at
io
n
I
t
is
ve
r
y
i
m
por
ta
nt
to
a
na
ly
z
e
a
nd
e
va
lu
a
te
th
e
r
e
s
ul
ts
a
f
te
r
a
ppl
yi
ng
th
e
di
f
f
e
r
e
nt
gr
a
ph
-
ba
s
e
d
m
e
th
ods
on
th
e
s
e
le
c
te
d
tr
a
ns
a
c
ti
on
da
ta
s
e
t.
T
hi
s
pha
s
e
a
id
s
u
s
r
e
a
li
z
e
th
e
e
f
f
ic
ie
nc
y
of
th
e
c
hos
e
n
a
ppr
oa
c
h,
m
e
a
s
ur
e
th
e
pe
r
f
or
m
a
nc
e
of
e
a
c
h
m
e
th
od,
a
nd
f
in
d
w
ha
t
m
us
t
be
im
pr
ove
d.
G
a
th
e
r
a
nd
e
xa
m
in
e
e
a
c
h
m
e
th
od'
s
out
put
a
c
c
or
di
ng
to
pr
e
de
te
r
m
in
e
d
a
s
s
e
s
s
m
e
nt
c
r
it
e
r
ia
.
T
he
s
e
c
r
it
e
r
ia
m
ig
ht
in
c
lu
de
out
c
om
e
s
in
te
r
pr
e
ta
bi
li
ty
,
c
om
put
a
ti
ona
l
e
f
f
ic
ie
nc
y,
s
c
a
l
a
bi
li
ty
in
m
a
na
g
in
g
bi
g
da
ta
s
e
t
s
,
a
nd
a
c
c
ur
a
c
y
of
tr
a
ns
a
c
ti
on
pa
tt
e
r
n r
e
c
ogni
ti
on.
3.5.
C
om
p
ar
is
on
T
he
pe
r
f
or
m
a
nc
e
of
th
e
c
hos
e
n
gr
a
ph
-
ba
s
e
d
m
e
th
ods
m
us
t
be
c
om
pa
r
e
d
de
pe
ndi
ng
on
f
iv
e
c
r
it
e
r
ia
,
th
e
y
a
r
e
:
s
c
a
la
bi
li
ty
,
a
c
c
ur
a
c
y,
c
om
pl
e
xi
ty
,
in
te
r
pr
e
ta
bi
li
ty
a
nd
ve
r
s
a
ti
li
ty
to
be
a
bl
e
to
de
te
r
m
in
e
w
hi
c
h
one
is
th
e
be
s
t
in
de
a
li
ng
w
it
h
tr
a
ns
a
c
ti
on
da
ta
s
e
t.
B
a
s
e
d
on
th
e
e
va
lu
a
ti
on
m
e
tr
ic
s
,
c
om
pa
r
e
how
w
e
ll
e
a
c
h
te
c
hni
que
pe
r
f
or
m
s
.
D
e
te
r
m
in
e
th
e
a
dva
nt
a
ge
s
a
nd
di
s
a
dv
a
nt
a
ge
s
of
e
a
c
h
a
ppr
oa
c
h
in
c
om
pa
r
is
on
to
th
e
ot
he
r
s
,
e
m
pha
s
iz
in
g
a
ny
c
om
pr
om
is
e
s
th
a
t
m
ig
ht
a
f
f
e
c
t
ho
w
w
e
ll
-
s
ui
te
d
e
a
c
h
is
f
or
a
gi
ve
n
ki
nd
of
tr
a
ns
a
c
ti
ona
l
da
ta
a
n
a
ly
s
is
.
3.6.
C
om
p
ar
at
iv
e
an
al
ys
is
o
f
gr
ap
h
-
b
as
e
d
m
e
t
h
od
s
G
r
a
ph
-
ba
s
e
d
m
e
th
ods
ha
ve
be
e
n
us
e
d
e
xt
e
ns
iv
e
ly
w
it
h
tr
a
ns
a
c
ti
on
da
ta
ba
s
e
s
.
F
or
th
is
c
om
pa
r
a
ti
ve
s
tu
dy,
w
e
f
oc
us
on
th
e
m
o
s
t
w
id
e
ly
us
e
d c
lo
s
e
n
-
ve
r
ti
c
e
s
a
dj
a
c
e
nc
y
gr
a
ph
r
e
pr
e
s
e
nt
a
ti
on.
T
hi
s
r
e
pr
e
s
e
nt
a
ti
on
de
f
in
e
s
a
gr
a
ph
w
he
r
e
e
a
c
h
nod
e
r
e
pr
e
s
e
nt
s
a
n
it
e
m
in
th
e
da
ta
ba
s
e
a
nd
n
-
ve
r
ti
c
e
s
a
r
e
qua
li
f
ie
d
a
s
a
dj
a
c
e
nt
to
e
a
c
h
ot
he
r
if
th
e
y
a
ppe
a
r
to
ge
th
e
r
in
a
tr
a
ns
a
c
ti
on.
I
t
is
a
ls
o
r
e
f
e
r
r
e
d
to
a
s
th
e
uni
que
-
it
e
m
s
e
t
-
c
ont
e
nt
-
c
om
pa
ti
bl
e
gr
a
ph (
U
C
C
gr
a
ph)
[
16]
, [
17]
.
R
e
ta
il
da
ta
s
e
t
is
one
of
th
e
popul
a
r
da
ta
s
e
t
s
us
e
d
in
da
ta
a
n
a
ly
s
is
a
nd
pa
tt
e
r
n
m
in
in
g
s
tu
di
e
s
in
r
e
ta
il
a
nd
s
a
le
s
.
T
hi
s
gr
oup
in
c
lu
de
s
da
ta
on
pur
c
ha
s
e
s
th
a
t
a
r
e
ty
pi
c
a
ll
y
r
e
c
or
de
d
th
r
ough
poi
nt
-
of
-
s
a
le
(
P
O
S
)
s
ys
te
m
s
i
n
s
to
r
e
s
a
nd
s
hops
. D
a
ta
u
s
ua
ll
y i
nc
lu
de
s
:
−
P
r
oduc
t
in
f
or
m
a
ti
on:
s
uc
h a
s
na
m
e
, de
s
c
r
ip
ti
on, a
nd c
a
te
gor
y.
−
C
us
to
m
e
r
in
f
or
m
a
ti
on:
s
uc
h a
s
a
ge
, g
e
nde
r
, a
nd l
oc
a
ti
on of
r
e
s
i
de
nc
e
.
−
P
ur
c
ha
s
e
de
ta
il
s
:
s
uc
h a
s
d
a
te
, t
im
e
, a
nd a
m
ount
pa
id
.
−
S
to
r
e
i
nf
or
m
a
ti
on:
s
uc
h a
s
l
oc
a
ti
on, br
a
nc
he
s
, a
nd de
p
a
r
tm
e
nt
s
.
−
P
a
ym
e
nt
m
e
th
ods
:
s
uc
h a
s
c
a
s
h, c
r
e
di
t
c
a
r
ds
, a
nd
e
le
c
tr
oni
c
pa
y
m
e
nt
.
U
s
in
g
a
r
e
ta
il
d
a
ta
s
e
t
c
a
n
he
lp
a
na
ly
z
e
c
us
to
m
e
r
pur
c
h
a
s
in
g
be
ha
vi
or
s
,
di
s
c
ove
r
c
om
m
on
pa
tt
e
r
ns
in
pur
c
ha
s
in
g,
f
or
e
c
a
s
t
pr
oduc
t
de
m
a
nd,
a
nd
im
pr
ove
in
ve
nt
or
y
m
a
na
ge
m
e
nt
a
nd
m
a
r
ke
ti
ng
s
tr
a
te
gi
e
s
.
T
hi
s
ki
t
is
id
e
a
l
f
or
r
e
s
e
a
r
c
h
s
tu
di
e
s
a
nd
bu
s
in
e
s
s
a
na
ly
s
is
in
th
e
r
e
ta
il
i
ndus
tr
y
[
16]
–
[
18]
.
I
t
w
il
l
be
e
f
f
ic
ie
nt
to
a
s
s
e
s
s
a
nd
s
e
le
c
t
th
e
b
e
s
t
gr
a
ph
-
ba
s
e
d
te
c
hni
que
f
or
ge
ne
r
a
ti
ng
r
ul
e
s
f
r
om
tr
a
ns
a
c
ti
ona
l
da
ta
s
e
ts
by
a
ppl
yi
ng
th
is
s
tr
uc
tu
r
e
d
c
om
pa
r
a
ti
ve
s
tu
dy,
c
ons
id
e
r
in
g
th
e
f
e
a
tu
r
e
s
of
th
e
da
ta
s
e
t
a
nd
th
e
us
e
r
s
'
uni
que
r
e
qui
r
e
m
e
nt
s
.
T
a
bl
e
2
is
a
n
e
xpa
nde
d
ta
bl
e
th
a
t
in
c
lu
de
s
th
e
e
va
lu
a
ti
on
f
or
e
a
c
h
m
e
th
od:
c
li
que
pe
r
c
ol
a
ti
on
s
y
s
te
m
,
a
dj
a
c
e
nc
y
m
a
tr
ix
,
ne
twor
k
-
ba
s
e
d
vi
s
ua
li
z
a
ti
on,
a
nd
G
N
N
.
T
hi
s
ta
bl
e
pr
ovi
de
s
a
c
om
pr
e
he
n
s
iv
e
ov
e
r
vi
e
w
of
how
e
a
c
h
m
e
th
od
is
e
va
lu
a
te
d
in
te
r
m
s
of
a
na
ly
s
i
s
,
vi
s
ua
li
z
a
ti
on,
a
nd
pr
e
di
c
ti
on
c
a
pa
bi
li
ti
e
s
ba
s
e
d
on
th
e
a
va
il
a
bl
e
da
ta
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
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8938
G
r
aph
-
bas
e
d m
e
th
od
s
f
or
tr
an
s
ac
ti
on databas
e
s
:
a c
om
par
at
iv
e
s
tu
dy
(
W
ae
l
A
hm
ad A
lZ
oubi
)
1667
T
a
bl
e
2.
T
he
e
va
lu
a
ti
on of
t
he
gr
a
ph
-
ba
s
e
d m
in
in
g m
e
th
od
s
f
r
om
t
r
a
ns
a
c
ti
on da
ta
s
e
t
s
M
e
t
hod
E
va
l
ua
t
i
on
D
e
t
a
i
l
s
of
e
va
l
ua
t
i
on
1.
C
l
i
que
pe
r
c
ol
a
t
i
on
s
ys
t
e
m
A
na
l
ys
i
s
of
di
s
c
ove
r
e
d
c
l
i
que
s
a
nd
c
om
pa
r
i
s
on
a
ga
i
ns
t
e
xpe
c
t
a
t
i
on
s
a
nd
r
e
qui
r
e
m
e
nt
s
E
va
l
ua
t
i
on
of
c
l
i
que
s
i
z
e
a
nd
f
r
e
que
nc
y
c
om
pa
r
i
s
on
a
c
r
os
s
va
r
i
ous
c
l
i
que
pe
r
c
ol
a
t
i
on s
y
s
t
e
m
s
e
t
t
i
ngs
(
e
.g., c
ha
ngi
ng k
i
f
a
ppl
i
c
a
bl
e
)
.
E
f
f
e
c
t
i
ve
ne
s
s
of
c
l
i
que
s
i
n
pr
e
di
c
t
i
ng
f
ut
ur
e
ne
t
w
or
k
or
da
t
a
be
ha
vi
or
.
2.
A
dj
a
c
e
nc
y
m
a
t
r
i
x
A
na
l
ys
i
s
of
r
e
l
a
t
i
on
s
hi
ps
be
t
w
e
e
n
c
a
t
e
gor
i
e
s
a
nd
m
e
a
s
ur
i
ng
r
e
l
a
t
i
ons
hi
p
s
t
r
e
ngt
hs
A
na
l
ys
i
s
of
e
xi
s
t
i
ng
r
e
l
a
t
i
ons
hi
ps
i
n
t
h
e
a
dj
a
c
e
n
c
y
m
a
t
r
i
x.
M
e
a
s
ur
e
m
e
nt
of
r
e
l
a
t
i
ons
hi
p
s
t
r
e
ngt
hs
be
t
w
e
e
n
c
a
t
e
gor
i
e
s
ba
s
e
d
on
va
l
ue
s
i
n
t
he
m
a
t
r
i
x.
C
om
p
a
r
i
s
on
of
a
dj
a
c
e
nc
y
m
a
t
r
i
c
e
s
unde
r
di
f
f
e
r
e
nt
ba
s
e
s
(
e
.g., qua
nt
i
t
y or
pr
i
c
e
)
.
3.
N
e
t
w
or
k
-
ba
s
e
d
v
i
s
ua
l
i
z
a
t
i
on
V
i
s
ua
l
unde
r
s
t
a
ndi
ng
of
r
e
l
a
t
i
ons
hi
ps
a
nd
r
e
pr
e
s
e
nt
a
t
i
on
of
de
ve
l
opm
e
nt
s
ove
r
time
V
i
s
ua
l
unde
r
s
t
a
ndi
ng
of
r
e
l
a
t
i
on
s
hi
ps
b
e
t
w
e
e
n
di
f
f
e
r
e
nt
c
a
t
e
gor
i
e
s
.
R
e
pr
e
s
e
nt
a
t
i
on
of
de
ve
l
opm
e
nt
s
ove
r
t
i
m
e
i
f
us
i
ng
t
e
m
por
a
l
ne
t
w
or
k
vi
s
ua
l
i
z
a
t
i
on.
C
om
p
a
r
i
s
on
of
di
f
f
e
r
e
nt
ne
t
w
or
k
vi
s
ua
l
i
z
a
t
i
ons
ba
s
e
d
on
dr
a
w
i
ng
t
e
c
hni
que
s
a
nd
e
m
pha
s
i
z
i
ng
ke
y
r
e
l
a
t
i
ons
hi
ps
be
t
w
e
e
n
c
a
t
e
gor
i
e
s
.
4.
GNN
I
m
pr
ove
m
e
nt
i
n
pr
oduc
t
c
a
t
e
gor
i
z
a
t
i
on
or
s
a
l
e
s
pr
e
di
c
t
i
on ba
s
e
d on
n
e
t
w
or
ks
E
va
l
ua
t
i
on
of
G
N
N
'
s
a
bi
l
i
t
y
t
o
c
ont
r
ol
ne
t
w
or
k
da
t
a
f
or
i
m
pr
ovi
ng
pr
oduc
t
c
a
t
e
gor
i
z
a
t
i
on
or
s
a
l
e
s
pr
e
di
c
t
i
on.
E
xa
m
i
na
t
i
on
of
G
N
N
'
s
pe
r
f
or
m
a
nc
e
i
n
l
e
a
r
ni
ng
i
nt
r
i
c
a
t
e
r
e
l
a
t
i
ons
hi
ps
be
t
w
e
e
n
c
a
t
e
gor
i
e
s
b
a
s
e
d
on
a
va
i
l
a
bl
e
da
t
a
.
C
om
pa
r
i
s
on of
G
N
N
r
e
s
ul
t
s
w
i
t
h t
r
a
di
t
i
ona
l
m
e
t
hods
.
4.
R
E
S
U
L
T
S
A
N
D
D
I
S
C
U
S
S
I
O
N
I
n
th
is
s
e
c
ti
on,
it
is
e
xpl
a
in
e
d
th
e
r
e
s
ul
ts
of
r
e
s
e
a
r
c
h
a
nd
a
t
th
e
s
a
m
e
ti
m
e
is
gi
v
e
n
th
e
c
om
pr
e
he
ns
iv
e
di
s
c
us
s
io
n.
R
e
s
ul
ts
c
a
n
be
pr
e
s
e
nt
e
d
in
f
ig
ur
e
s
,
gr
a
phs
,
ta
bl
e
s
a
nd
ot
he
r
s
th
a
t
m
a
ke
th
e
r
e
a
de
r
unde
r
s
ta
nd
e
a
s
il
y
[
19]
,
[
20]
.
I
n
th
e
li
te
r
a
tu
r
e
[
21]
–
[
25]
,
th
e
r
e
a
r
e
m
a
ny
s
tu
di
e
s
a
bout
th
e
di
f
f
e
r
e
nt
gr
a
ph
ba
s
e
d
m
e
th
ods
f
or
tr
a
ns
a
c
ti
on
da
ta
s
e
t
s
,
w
e
u
s
e
d
th
e
s
a
m
e
s
e
t
of
da
ta
f
or
e
a
c
h
m
e
th
od
unde
r
in
ve
s
ti
ga
ti
on
dur
in
g t
he
c
om
pa
r
is
on a
na
ly
s
is
. T
hi
s
m
e
th
odol
ogy gua
r
a
nt
e
e
s
i
m
pa
r
ti
a
li
ty
a
nd unif
o
r
m
it
y w
hi
le
a
s
s
e
s
s
in
g t
he
e
f
f
ic
a
c
y of
va
r
io
us
gr
a
ph
-
ba
s
e
d t
e
c
hni
que
s
f
or
t
r
a
ns
a
c
ti
on da
ta
s
e
t
m
in
in
g.
F
iv
e
di
f
f
e
r
e
nt
c
r
it
e
r
ia
w
e
r
e
us
e
d
to
of
f
e
r
a
c
om
pl
e
te
s
tr
uc
tu
r
e
f
or
a
ll
oc
a
ti
ng
num
be
r
s
to
th
e
ta
bl
e
s
th
a
t
r
e
f
le
c
ts
a
n
e
xha
u
s
ti
ve
e
va
lu
a
ti
on
of
th
e
e
f
f
e
c
ti
ve
ne
s
s
of
e
a
c
h
te
c
hni
que
in
r
e
la
ti
on
to
ne
twor
k
da
ta
a
na
ly
s
is
a
nd vi
s
ua
li
z
a
ti
on
[
4]
,
[
26]
. T
he
c
r
it
e
r
ia
a
r
e
:
−
S
c
a
la
bi
li
ty
:
a
s
s
e
s
s
e
s
how
w
e
ll
e
a
c
h
te
c
hni
que
c
a
n
m
a
n
a
g
e
in
c
r
e
a
s
in
g
a
m
ount
s
of
da
ta
w
it
hout
s
a
c
r
if
ic
in
g e
f
f
ic
ie
nc
y a
nd c
onc
e
r
t.
−
C
om
pl
e
xi
ty
:
e
va
lu
a
te
s
e
a
c
h m
e
th
od'
s
c
om
put
a
ti
ona
l
c
os
t
a
nd r
e
s
our
c
e
us
a
g
e
(
m
e
m
or
y a
nd C
P
U
t
im
e
)
.
−
A
c
c
ur
a
c
y:
e
va
lu
a
te
s
e
a
c
h
m
e
th
od'
s
c
a
p
a
c
it
y
to
pr
oduc
e
a
c
c
u
r
a
te
a
nd
de
pe
nd
a
bl
e
out
c
om
e
s
in
ta
s
ks
in
vol
vi
ng i
nve
s
ti
ga
ti
on a
nd pr
e
s
e
nt
a
ti
on.
−
I
nt
e
r
pr
e
ta
bi
li
ty
:
e
va
lu
a
te
s
th
e
e
a
s
e
of
c
om
pr
e
he
n
s
io
n
a
nd
in
te
r
pr
e
ta
ti
on
of
th
e
out
put
s
a
nd
out
c
om
e
s
pr
oduc
e
d by e
a
c
h m
e
th
od.
−
V
e
r
s
a
ti
li
ty
:
e
xa
m
in
e
s
t
he
a
d
a
pt
a
bi
li
ty
of
e
a
c
h m
e
th
od t
o a
br
oa
d r
a
nge
of
a
c
ti
vi
ti
e
s
a
nd a
ppl
ic
a
ti
ons
.
E
a
c
h
of
th
e
s
e
c
r
it
e
r
ia
w
il
l
be
te
s
te
d
s
e
p
a
r
a
te
ly
f
or
e
a
c
h
of
th
e
s
e
m
e
th
ods
a
nd
th
e
n
th
e
r
e
s
ul
ts
w
il
l
be
c
om
pa
r
e
d a
s
i
n t
he
f
ol
lo
w
in
g s
e
c
ti
on
s
.
4.1.
S
c
al
ab
il
it
y
E
a
c
h
m
e
th
od'
s
s
c
a
la
bi
li
ty
di
f
f
e
r
s
gr
e
a
tl
y
de
pe
ndi
ng
on
how
it
is
de
s
ig
ne
d
a
nd
in
te
nde
d
to
be
us
e
d.
T
he
m
ode
s
t
s
c
a
la
bi
li
ty
of
th
e
c
li
que
pe
r
c
ol
a
ti
on
s
ys
te
m
m
a
ke
s
it
a
ppr
opr
ia
te
f
or
m
e
di
um
-
s
iz
e
d
ne
twor
ks
,
but
it
m
ig
ht
be
pr
obl
e
m
a
ti
c
f
o
r
ve
r
y
la
r
ge
da
ta
s
e
ts
[
26]
,
[
27]
.
T
h
e
a
dj
a
c
e
nc
y
m
a
tr
ix
,
on
th
e
ot
he
r
ha
nd,
s
how
s
good
s
c
a
la
bi
li
ty
a
nd
is
e
f
f
e
c
ti
ve
f
or
bi
g,
s
ta
ti
c
ne
twor
ks
,
but
it
c
oul
d
ne
e
d a
lo
t
of
a
s
s
e
t
s
f
or
ne
twor
ks
th
a
t
a
r
e
dyna
m
ic
[
27]
.
W
he
n
pr
ope
r
ly
de
s
ig
ne
d,
th
e
G
N
N
e
xhi
bi
ts
s
ig
ni
f
ic
a
nt
s
c
a
la
bi
li
ty
a
s
w
e
ll
,
m
a
ki
ng
it
a
vi
a
bl
e
opt
io
n
f
or
e
f
f
ic
ie
nt
ly
pr
oc
e
s
s
in
g
huge
da
ta
s
e
ts
[
28]
,
[
29]
.
D
e
pe
ndi
ng
on
th
e
a
m
ount
of
th
e
da
ta
s
e
t
a
nd
th
e
di
s
pl
a
y
c
a
p
a
bi
li
ti
e
s
,
ne
twor
k
-
ba
s
e
d
vi
s
ua
li
z
a
ti
on
[
30]
pr
ovi
de
s
s
tr
ong
s
c
a
la
bi
li
ty
f
or
vi
s
ua
l
e
xpl
or
a
ti
on,
m
a
ki
ng
it
e
a
s
ie
r
f
or
us
e
r
s
to
e
xpl
or
e
ne
twor
k
s
tr
uc
tu
r
e
s
e
a
s
il
y
.
T
he
s
e
f
in
di
ngs
a
id
in
th
e
s
ui
ta
bl
e
te
c
hni
que
c
hoos
in
g, c
ons
id
e
r
in
g t
he
s
c
a
la
bi
li
ty
r
e
qui
r
e
m
e
nt
s
f
or
a
na
ly
s
is
or
vi
s
ua
li
z
a
ti
on c
hor
e
s
.
B
a
s
e
d
on
th
e
a
ll
oc
a
t
e
d
num
e
r
ic
a
l
va
lu
e
s
,
th
is
r
e
pr
e
s
e
nt
a
ti
o
n
m
a
ke
s
it
e
a
s
ie
r
f
or
c
ons
um
e
r
s
or
r
e
s
e
a
r
c
he
r
s
to
unde
r
s
t
a
nd
how
th
e
pr
oc
e
dur
e
s
di
f
f
e
r
f
r
om
on
e
a
not
he
r
in
a
m
or
e
s
tr
uc
tu
r
e
d
w
a
y.
I
t
m
a
ke
s
de
c
is
io
n
-
m
a
ki
ng
e
a
s
i
e
r
de
pe
ndi
ng
on
c
e
r
ta
in
a
na
ly
s
i
s
r
e
qui
r
e
m
e
nt
s
or
in
te
nde
d
r
e
s
ul
t
s
.
F
ig
ur
e
2
a
nd
T
a
bl
e
3
il
lu
s
tr
a
te
gr
a
phi
c
a
ll
y t
he
s
c
a
la
bi
li
ty
of
e
a
c
h on
e
of
t
he
s
e
m
e
th
od
s
on t
he
s
e
le
c
te
d r
e
ta
il
da
ta
s
e
t.
4.2. Com
p
le
xi
t
y
T
h
e
c
om
pl
e
xi
ty
de
gr
e
e
of
e
a
c
h
m
e
th
od
i
s
s
ho
w
n
b
y
th
e
"
c
om
pl
e
xi
t
y
"
r
e
s
u
lt
s
.
T
h
e
c
li
q
u
e
p
e
r
c
o
l
a
t
io
n
s
y
s
t
e
m
e
xh
ib
it
s
lo
w
c
o
m
p
l
e
x
it
y
b
y
u
s
in
g
s
i
m
p
l
e
m
e
t
h
od
s
th
a
t
a
r
e
e
f
f
e
c
t
iv
e
in
t
e
r
m
s
of
p
r
o
c
e
s
s
i
n
g
s
p
e
e
d
a
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
2025
:
1663
-
1672
1668
m
e
m
o
r
y
ut
il
i
z
a
t
io
n.
T
h
e
c
om
pl
e
xi
ty
of
th
e
a
dj
a
c
e
nc
y
m
a
tr
ix
r
a
n
g
e
s
f
r
o
m
l
o
w
t
o
r
e
a
s
on
a
bl
e
,
d
e
p
e
n
di
n
g
o
n
t
h
e
e
x
t
e
n
t
of
th
e
e
nt
ir
e
ne
t
w
o
r
k
a
nd
m
e
m
or
y
n
e
e
d
s
[
3
1]
.
B
e
c
a
u
s
e
t
h
e
y
e
m
pl
oy
d
e
e
p
l
e
a
r
ni
ng
t
e
c
h
ni
q
ue
s
,
G
N
N
s
e
x
h
ib
it
e
n
or
m
o
u
s
c
om
pl
e
xi
ty
,
r
e
qu
ir
in
g
s
u
b
s
t
a
nt
ia
l
pr
o
c
e
s
s
i
ng
r
e
s
o
u
r
c
e
s
a
n
d
a
l
e
n
g
th
y
tr
a
i
ni
n
g
pe
r
i
od
[
7]
,
[
3
2]
.
N
e
t
w
o
r
k
-
b
a
s
e
d
v
i
s
u
a
li
z
a
t
i
on
i
s
lo
w
to
m
od
e
r
a
t
e
l
y
c
om
pl
ic
a
t
e
d
,
w
i
th
s
i
m
p
l
e
d
i
s
pl
a
y
o
p
e
r
a
t
i
on
s
a
t
th
e
b
a
s
e
[
33
]
.
L
a
r
g
e
n
e
t
w
o
r
k
s
o
r
i
n
te
r
a
c
ti
v
e
f
u
nc
ti
o
n
a
li
t
y m
a
y
c
a
l
l
f
o
r
a
d
di
ti
o
na
l
r
e
s
o
ur
c
e
s
.
T
he
f
in
di
ng
s
s
h
e
d
li
g
ht
o
n
ho
w
e
a
c
h
t
e
c
hn
iq
u
e
m
a
n
a
g
e
s
t
h
e
c
om
pl
e
xi
ty
a
n
d
pr
o
c
e
s
s
i
ng
d
e
m
a
n
d
s
of
ne
t
w
or
k
da
t
a
a
na
l
y
s
i
s
a
n
d
vi
s
ua
li
z
a
ti
on
.
F
i
gu
r
e
3
a
n
d
T
a
b
l
e
4
il
lu
s
tr
a
te
gr
a
p
hi
c
a
ll
y
th
e
c
o
m
p
l
e
x
it
y
of
e
a
c
h
o
n
e
of
t
he
s
e
m
e
t
ho
d
s
o
n
th
e
s
e
l
e
c
t
e
d
r
e
t
a
i
l
d
a
t
a
s
e
t.
F
ig
ur
e
2. G
r
a
phi
c
a
l
r
e
pr
e
s
e
nt
a
ti
on of
t
he
s
c
a
la
bi
li
ty
a
m
ong the
gr
a
ph
-
ba
s
e
d m
e
th
ods
f
or
r
e
ta
il
da
ta
s
e
t
F
ig
ur
e
3. G
r
a
phi
c
a
l
r
e
pr
e
s
e
nt
a
ti
on of
t
he
c
om
pl
e
xi
ty
a
m
ong the
gr
a
ph
-
ba
s
e
d m
e
th
ods
f
or
r
e
ta
il
da
ta
s
e
t
T
a
bl
e
3. S
c
a
la
bi
li
ty
of
gr
a
ph
-
ba
s
e
d m
e
th
od
s
M
e
t
hod
S
c
a
l
a
bi
l
i
t
y
C
l
i
que
pe
r
c
ol
a
t
i
on s
ys
t
e
m
3
A
dj
a
c
e
nc
y
m
a
t
r
i
x
4
GNN
4
N
e
t
w
or
k
-
ba
s
e
d
v
i
s
ua
l
i
z
a
t
i
on
3
E
xpl
a
na
t
i
on of
va
l
ue
s
:
S
c
a
l
a
bi
l
i
t
y:
1:
L
ow
s
c
a
l
a
bi
l
i
t
y
2:
M
ode
r
a
t
e
s
c
a
l
a
bi
l
i
t
y
3:
H
i
gh s
c
a
l
a
bi
l
i
t
y
4:
S
c
a
l
a
bl
e
f
or
l
a
r
ge
da
t
a
s
e
t
s
5:
H
i
ghl
y s
c
a
l
a
bl
e
w
i
t
h a
ppr
opr
i
a
t
e
a
r
c
hi
t
e
c
t
ur
e
T
a
bl
e
4. C
om
pl
e
xi
ty
of
gr
a
ph
-
ba
s
e
d m
e
th
od
s
M
e
t
hod
C
om
pl
e
xi
t
y
C
l
i
que
pe
r
c
ol
a
t
i
on s
ys
t
e
m
1
A
dj
a
c
e
nc
y
m
a
t
r
i
x
2
GNN
5
N
e
t
w
or
k
-
ba
s
e
d
v
i
s
ua
l
i
z
a
t
i
on
2
E
xpl
a
na
t
i
on of
v
a
l
ue
s
:
C
om
pl
e
xi
t
y
1:
L
ow
c
om
pl
e
xi
t
y
2:
L
ow
t
o m
ode
r
a
t
e
c
om
pl
e
xi
t
y
3:
M
ode
r
a
t
e
c
om
pl
e
xi
t
y
4:
H
i
gh c
om
pl
e
xi
t
y due
t
o de
e
p l
e
a
r
ni
ng t
e
c
hni
que
s
5:
V
e
r
y hi
gh c
om
pl
e
xi
t
y
4.3.
A
c
c
u
r
ac
y
T
he
"
a
c
c
ur
a
c
y"
r
e
s
ul
t
s
s
how
how
a
c
c
ur
a
te
e
a
c
h
m
e
th
od
is
.
T
h
e
c
li
que
pe
r
c
ol
a
ti
on
s
ys
t
e
m
is
a
good
to
ol
f
or
r
e
c
ogni
z
in
g
c
om
m
uni
ti
e
s
w
it
hi
n
ne
twor
ks
s
in
c
e
it
s
how
s
good
a
c
c
ur
a
c
y
in
id
e
nt
if
yi
ng
c
ohe
s
iv
e
gr
oups
,
or
c
li
que
s
.
T
he
a
dj
a
c
e
nc
y
m
a
tr
ix
is
a
vi
s
ua
l
a
id
th
a
t
m
a
ke
s
node
c
onne
c
ti
on
s
e
a
s
ie
r
to
unde
r
s
ta
nd
w
hi
le
of
f
e
r
in
g
e
xc
e
ll
e
nt
a
c
c
ur
a
c
y
in
c
om
put
in
g
ne
twor
k
m
e
tr
i
c
s
li
ke
node
de
gr
e
e
s
a
nd
s
hor
te
s
t
pa
th
s
[
27]
.
W
he
n
le
a
r
ni
ng
node
a
nd
e
dge
f
e
a
tu
r
e
s
,
G
N
N
s
de
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te
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tt
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n
r
e
c
ogni
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ppl
ic
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ti
ons
[
7]
,
[
29]
–
[
31]
.
D
e
pe
ndi
ng
on
th
e
m
e
th
ods
us
e
d
a
nd
th
e
le
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l
of
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e
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xpe
r
ie
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k
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s
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ti
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ts
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e
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gh
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y
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k
a
r
c
hi
te
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tu
r
e
a
nd
s
pot
ti
ng
pa
tt
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r
ns
[
33]
.
T
he
s
e
poi
nt
s
de
m
o
ns
tr
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te
how
e
a
c
h
te
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hni
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om
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or
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ur
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xa
m
in
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g
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nd
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s
pl
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yi
ng
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e
twor
k
da
ta
.
F
ig
ur
e
4
a
nd
T
a
bl
e
5
il
lu
s
tr
a
te
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a
phi
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a
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he
c
om
pl
e
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ty
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e
a
c
h one
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he
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e
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e
th
ods
on t
he
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le
c
te
d r
e
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il
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4.4. I
n
t
e
r
p
r
e
t
ab
il
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y
T
he
te
r
m
"
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te
r
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ib
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e
out
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om
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e
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od
[
4]
,
[
26]
.
B
e
c
a
us
e
th
e
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li
que
pe
r
c
ol
a
ti
on
s
ys
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m
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in
ly
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ds
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ohe
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gr
oups
0
1
2
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4
5
Cl
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P
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S
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G
r
a
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r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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8938
G
r
aph
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bas
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e
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ont
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s
lo
w
in
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r
pr
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ta
bi
li
ty
[
27]
.
T
h
e
a
dj
a
c
e
nc
y
m
a
tr
ix
,
on
th
e
ot
he
r
ha
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pr
ovi
de
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pr
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li
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a
phi
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a
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onn
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a
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pos
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om
pr
e
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k
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c
onne
c
ti
ons
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nd
s
tr
uc
tu
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e
w
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h
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la
r
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y
[
28]
.
G
iv
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th
a
t
t
he
y
le
a
r
n
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tr
ic
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te
node
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h
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or
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pt
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e
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r
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ope
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ly
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xhi
bi
t
in
te
r
m
e
di
a
te
in
te
r
p
r
e
ta
bi
li
ty
[
7]
,
[
29]
–
[
34]
.
H
ig
h
in
te
r
pr
e
ta
bi
li
ty
is
a
c
hi
e
ve
d
us
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k
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ba
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por
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ti
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s
ta
ndi
ng
of
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twor
k
to
pol
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a
nd
pa
tt
e
r
ns
[
35]
.
T
he
s
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va
r
ia
ti
ons
hi
ghl
ig
ht
how
th
e
in
te
r
pr
e
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li
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of
e
a
c
h
a
ppr
oa
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h
m
e
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ts
va
r
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us
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e
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e
m
e
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s
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or
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f
ic
ie
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unde
r
s
ta
ndi
ng
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na
ly
z
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g
ne
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k
da
ta
.
F
ig
ur
e
5
a
nd
T
a
bl
e
6
il
lu
s
tr
a
te
gr
a
phi
c
a
ll
y t
he
i
nt
e
r
pr
e
ta
bi
li
ty
of
e
a
c
h one
of
t
he
s
e
m
e
th
ods
on
th
e
s
e
le
c
te
d r
e
ta
il
da
t
a
s
e
t.
F
ig
ur
e
4. G
r
a
phi
c
a
l
r
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pr
e
s
e
nt
a
ti
on of
t
he
a
c
c
ur
a
c
y a
m
ong the
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r
a
ph
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s
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d m
e
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ods
f
or
r
e
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da
ta
s
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t
F
ig
ur
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5. G
r
a
phi
c
a
l
r
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pr
e
s
e
nt
a
ti
on of
t
he
i
nt
e
r
pr
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ta
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li
ty
a
m
ong the
gr
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ph
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ba
s
e
d m
e
th
ods
f
or
r
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il
da
ta
s
e
t
T
a
bl
e
5. A
c
c
ur
a
c
y of
gr
a
ph
-
ba
s
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d m
e
th
ods
M
e
t
hod
A
c
c
ur
a
c
y
C
l
i
que
pe
r
c
ol
a
t
i
on s
ys
t
e
m
4
A
dj
a
c
e
nc
y
m
a
t
r
i
x
5
GNN
5
N
e
t
w
or
k
-
ba
s
e
d
v
i
s
ua
l
i
z
a
t
i
on
4
E
xpl
a
na
t
i
on of
va
l
ue
s
:
A
c
c
ur
a
c
y:
1:
L
ow
a
c
c
ur
a
c
y
2:
L
ow
t
o
m
e
di
um
a
c
c
ur
a
c
y
3:
M
e
di
um
a
c
c
ur
a
c
y
4:
H
i
gh a
c
c
ur
a
c
y
5:
V
e
r
y hi
gh a
c
c
ur
a
c
y
T
a
bl
e
6. I
nt
e
r
pr
e
ta
bi
li
ty
of
gr
a
ph
-
ba
s
e
d m
e
th
ods
M
e
t
hod
I
nt
e
r
pr
e
t
a
bi
l
i
t
y
C
l
i
que
pe
r
c
ol
a
t
i
on s
ys
t
e
m
2
A
dj
a
c
e
nc
y
m
a
t
r
i
x
4
GNN
3
N
e
t
w
or
k
-
ba
s
e
d
v
i
s
ua
l
i
z
a
t
i
on
5
E
xpl
a
na
t
i
on of
va
l
ue
s
:
I
nt
e
r
pr
e
t
a
bi
l
i
t
y
:
1:
L
ow
i
nt
e
r
pr
e
t
a
bi
l
i
t
y
2:
M
ode
r
a
t
e
i
nt
e
r
pr
e
t
a
bi
l
i
t
y
3:
H
i
gh i
nt
e
r
pr
e
t
a
bi
l
i
t
y
4:
H
i
gh i
nt
e
r
pr
e
t
a
bi
l
i
t
y;
m
a
t
r
i
x f
or
m
a
t
vi
s
ua
l
l
y r
e
pr
e
s
e
nt
s
node
c
onne
c
t
i
ons
5:
H
i
ghl
y i
nt
e
r
pr
e
t
a
bl
e
;
pr
ovi
de
s
ba
s
i
c
vi
s
ua
l
i
ns
i
ght
s
4.5.
V
e
r
s
at
il
it
y
T
h
e
d
e
gr
e
e
t
o
w
h
ic
h a
m
e
t
hod
c
a
n b
e
t
a
i
lo
r
e
d t
o a
va
r
ie
ty
of
a
c
ti
vi
ti
e
s
a
nd
a
pp
li
c
a
ti
o
n
s
i
s
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e
f
e
r
r
e
d t
o a
s
it
s
v
e
r
s
a
ti
l
it
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. W
i
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it
s
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a
r
r
o
w
s
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o
pe
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li
c
a
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li
ty
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he
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li
qu
e
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e
r
c
ol
a
ti
on
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y
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t
e
m
i
s
m
a
i
nl
y
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s
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l
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or
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tu
d
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n
g
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g
a
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e
d
gr
o
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or
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ir
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he
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e
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e
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ti
on
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e
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e
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w
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k
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n
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t
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c
om
put
a
ti
on
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di
f
f
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m
e
tr
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c
s
,
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e
a
dj
a
c
e
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y
m
a
tr
ix
pr
o
vi
d
e
s
go
od
a
d
a
pt
a
b
il
i
ty
[
3
6]
.
G
N
N
s
a
r
e
ve
r
y
v
e
r
s
a
ti
l
e
;
t
he
y
c
a
n
h
a
nd
le
a
w
id
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ng
e
o
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bs
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a
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e
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c
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ni
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e
in
tr
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c
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t
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p
a
tt
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s
a
n
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t
to
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a
r
i
ou
s
k
in
d
s
of
n
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or
k
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nput
[
37]
,
[
3
8]
.
A
dd
it
i
on
a
ll
y,
n
e
t
w
or
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b
a
s
e
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s
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r
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e
a
t
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a
r
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y
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e
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bl
i
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te
r
a
c
ti
ve
a
nd
v
is
ua
l
n
e
t
w
or
k
e
x
pl
or
a
ti
o
n
a
n
d
a
n
a
l
y
s
i
s
,
w
hi
c
h
m
a
k
e
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it
e
a
s
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to
f
ul
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c
om
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e
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ne
tw
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k
p
a
t
te
r
n
s
a
nd
s
tr
u
c
tu
r
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s
[
3
9]
.
T
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e
d
if
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e
r
e
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s
ho
w
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5
Cl
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P
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S
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A
d
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Ma
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r
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r
a
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wo
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G
N
N
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b
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V
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
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J
A
r
ti
f
I
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.
14
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S
[
1]
M
.
B
e
s
t
a
e
t
al
.
,
“
D
e
m
y
s
t
i
f
yi
ng
gr
a
ph
da
t
a
ba
s
e
s
:
a
na
l
ys
i
s
a
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a
xonom
y
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or
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ni
z
a
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on,
s
ys
t
e
m
de
s
i
gns
,
a
nd
gr
a
ph
qu
e
r
i
e
s
,
”
A
C
M
C
om
put
i
ng Sur
v
e
y
s
, vol
. 56, no. 2, pp. 1
–
40, 2024, doi
:
10.1145/
3604932
.
[
2]
Y
.
S
ha
o
a
nd
N
.
N
a
ka
s
hol
e
,
“
O
n
l
i
ne
a
r
i
z
i
ng
s
t
r
uc
t
ur
e
d
da
t
a
i
n
e
n
c
ode
r
-
de
c
ode
r
l
a
ngua
ge
m
ode
l
s
:
i
ns
i
ght
s
f
r
om
t
e
xt
-
to
-
S
Q
L
,”
i
n
P
r
oc
e
e
di
ngs
of
t
h
e
2024
C
onf
e
r
e
nc
e
of
t
he
N
or
t
h
A
m
e
r
i
c
an
C
hapt
e
r
of
t
he
A
s
s
oc
i
at
i
on
f
or
C
om
put
at
i
onal
L
i
ngui
s
t
i
c
s
:
H
um
an
L
anguage
T
e
c
hnol
ogi
e
s
, 2024, pp. 131
–
156, doi
:
10.18653/
v1/
2024.na
a
c
l
-
l
ong.8.
[
3]
M
.
E
.
C
oi
m
br
a
,
A
.
P
.
F
r
a
nc
i
s
c
o,
a
nd
L
.
V
e
i
ga
,
“
S
t
udy
on
r
e
s
our
c
e
e
f
f
i
c
i
e
nc
y
of
di
s
t
r
i
but
e
d
gr
a
ph
pr
oc
e
s
s
i
ng,”
ar
X
i
v
-
C
om
put
e
r
Sc
i
e
nc
e
, pp. 1
–
23, 2017.
[
4]
A
.
B
a
udi
n,
M
.
D
a
ni
s
c
h,
S
.
K
i
r
gi
z
ov,
C
.
M
a
gni
e
n,
a
nd
M
.
G
ha
ne
m
,
“
C
l
i
que
p
e
r
c
ol
a
t
i
on
m
e
t
hod:
m
e
m
or
y
e
f
f
i
c
i
e
nt
a
l
m
os
t
e
xa
c
t
c
om
m
uni
t
i
e
s
,”
i
n
A
dv
anc
e
d D
at
a M
i
ni
ng and A
ppl
i
c
at
i
ons
, 2022, pp. 113
–
127.
[
5]
J
.
K
i
m
,
S
.
L
e
e
,
Y
.
K
i
m
,
S
.
A
hn,
a
nd
S
.
C
ho,
“
G
r
a
ph
l
e
a
r
ni
ng
-
ba
s
e
d
bl
oc
kc
ha
i
n
phi
s
hi
ng
a
c
c
ount
de
t
e
c
t
i
on
w
i
t
h
a
he
t
e
r
oge
ne
ous
t
r
a
ns
a
c
t
i
on gr
a
ph,”
Se
ns
o
r
s
, vol
. 23, no. 1, 2023, doi
:
10.3390/
s
23010463.
[
6]
X
.
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m
a
t
r
i
x
r
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pr
e
s
e
nt
a
t
i
on
l
e
a
r
ni
ng
f
or
m
ul
t
i
va
r
i
a
t
e
t
i
m
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s
e
r
i
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s
i
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r
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on
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w
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ppr
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T
r
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on
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dge
gr
a
ph
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s
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a
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c
h
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f
or
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t
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hm
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de
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t
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U
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na
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ul
t
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s
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r
i
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gr
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A
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c
a
t
i
ons
t
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a
r
d
di
s
c
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va
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i
a
bi
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S
A
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r
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a
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t
s
a
ppl
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t
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C
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Saf
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L
i
u
e
t
al
.
,
“
S
ur
ve
y
on
gr
a
ph
ne
ur
a
l
ne
t
w
or
k
a
c
c
e
l
e
r
a
t
i
on:
a
n
a
l
gor
i
t
hm
i
c
pe
r
s
pe
c
t
i
ve
,”
i
n
I
J
C
A
I
I
nt
e
r
nat
i
onal
J
oi
nt
C
onf
e
r
e
nc
e
on A
r
t
i
f
i
c
i
al
I
nt
e
l
l
i
ge
nc
e
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–
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i
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c
a
i
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V
.
Y
oghour
dj
i
a
n,
Y
.
Y
a
ng,
T
.
D
w
ye
r
,
L
.
L
a
w
r
e
nc
e
,
M
.
W
ybr
ow
,
a
nd
K
.
M
a
r
r
i
ot
t
,
“
S
c
a
l
a
bi
l
i
t
y
o
f
ne
t
w
or
k
v
i
s
ua
l
i
s
a
t
i
on
f
r
om
a
c
ogni
t
i
ve
l
oa
d
pe
r
s
pe
c
t
i
ve
,”
I
E
E
E
T
r
ans
ac
t
i
ons
on
V
i
s
ual
i
z
at
i
on
and
C
om
put
e
r
G
r
aphi
c
s
,
vol
.
27,
no.
2,
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1677
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1687,
2021,
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M
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l
a
w
a
t
s
c
h,
M
.
B
ur
c
h, a
nd
D
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e
i
s
kopf
, “
V
i
s
u
a
l
a
dj
a
c
e
nc
y l
i
s
t
s
f
or
dyna
m
i
c
gr
a
phs
,”
I
E
E
E
T
r
ans
ac
t
i
ons
on V
i
s
ual
i
z
at
i
on
and
C
om
put
e
r
G
r
aphi
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S
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Z
ha
ng,
H
.
T
ong,
J
.
X
u,
a
nd
R
.
M
a
c
i
e
j
e
w
s
ki
,
“
G
r
a
ph
c
onvol
ut
i
ona
l
ne
t
w
or
k
s
:
a
c
om
pr
e
he
ns
i
ve
r
e
vi
e
w
,
”
C
om
put
at
i
onal
So
c
i
al
N
e
t
w
or
k
s
, vol
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:
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s
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[
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I
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m
a
r
a
l
, “
C
om
pl
e
x ne
t
w
or
ks
,”
i
n
E
nc
y
c
l
ope
di
a of
B
i
g D
at
a
, C
ha
m
:
S
pr
i
nge
r
I
nt
e
r
na
t
i
ona
l
P
ubl
i
s
hi
ng, 2022, pp. 198
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[
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H
.
X
ua
nyua
n,
P
.
B
a
r
bi
e
r
o,
D
.
G
e
or
gi
e
v,
L
.
C
.
M
a
gi
s
t
e
r
,
a
nd
P
.
L
i
ò,
“
G
l
ob
a
l
c
onc
e
pt
-
ba
s
e
d
i
nt
e
r
pr
e
t
a
bi
l
i
t
y
f
o
r
g
r
a
ph
ne
ur
a
l
ne
t
w
or
ks
vi
a
ne
ur
on
a
n
a
l
ys
i
s
,”
P
r
oc
e
e
di
ng
s
of
t
he
37t
h
A
A
A
I
C
onf
e
r
e
nc
e
on
A
r
t
i
f
i
c
i
al
I
nt
e
l
l
i
ge
nc
e
,
A
A
A
I
2023
,
vol
.
37,
no.
9,
pp. 10675
–
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a
a
i
.v37i
9.26267.
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H
. R
a
w
l
a
ni
, “
V
i
s
u
a
l
i
nt
e
r
pr
e
t
a
bi
l
i
t
y f
or
c
onvol
ut
i
ona
l
ne
ur
a
l
ne
t
w
or
k,”
T
ow
ar
ds
D
at
a Sc
i
e
nc
e
, pp. 1
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20, 2018.
[
36]
M
.
L
i
,
Y
.
D
e
ng,
a
nd
B
.
H
.
W
a
ng,
“
C
l
i
que
pe
r
c
ol
a
t
i
on
i
n
r
a
ndom
gr
a
phs
,”
P
hy
s
i
c
al
R
e
v
i
e
w
E
-
St
at
i
s
t
i
c
al
,
N
onl
i
ne
a
r
,
and
Sof
t
M
at
t
e
r
P
hy
s
i
c
s
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P
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R
e
vE
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I
.
R
.
W
a
r
d, J
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oyne
r
,
C
.
L
i
c
kf
ol
d,
Y
.
G
uo,
a
nd
M
.
B
e
nna
m
oun,
“
A
pr
a
c
t
i
c
a
l
t
u
t
or
i
a
l
on
g
r
a
ph
ne
ur
a
l
ne
t
w
or
ks
,”
A
C
M
C
om
put
i
ng
Sur
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B
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h
e
m
a
ni
,
S
.
P
a
t
i
l
,
K
.
K
o
t
e
c
ha
, a
nd
S
.
T
a
n
w
a
r
, “
A
r
e
v
i
e
w
o
f
g
r
a
ph
ne
ur
a
l
ne
t
w
or
ks
:
c
onc
e
p
t
s
, a
r
c
hi
t
e
c
t
u
r
e
s
,
t
e
c
hn
i
q
ue
s
,
c
ha
l
l
e
ng
e
s
,
da
t
a
s
e
t
s
,
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p
pl
i
c
a
t
i
ons
,
a
n
d
f
u
t
u
r
e
di
r
e
c
t
i
ons
,”
J
our
na
l
o
f
B
i
g
D
a
t
a
,
v
ol
. 1
1,
no
.
1,
2
024
, d
oi
:
10.
11
86
/
s
40
537
-
023
-
008
76
-
4.
[
3
9]
S
.
D
u
t
t
a
a
n
d
S
.
R
oy
, “
C
om
pl
e
x
ne
t
w
o
r
k
vi
s
ua
l
i
s
a
t
i
on
us
i
ng
J
a
va
S
c
r
i
pt
:
a
r
e
v
i
e
w
,
”
i
n
I
nt
e
l
l
i
g
e
n
t
S
y
s
t
e
m
s
,
vo
l
.
43
1,
20
22,
p
p.
45
–
53
.
B
I
O
G
R
A
P
H
I
E
S
O
F
A
U
T
H
O
R
S
Wael
Ahmad
AlZoubi
holds
a
doctor
of
computer
sciences
f
rom
Nationa
l
University of Mal
aysia in 2013. He al
so received hi
s B.Sc. and M.
Sc.
(
computer
science
) from
Yarmouk
University,
Jordan
in
2000
and
2004,
respectively.
He
is
currently
an
Assistan
t
Profes
sor
at
Department
of
Computer
Science
in
Al
-
Balqa
Appli
ed
University,
Ajloun,
Jordan.
His
researc
h
includes
meta
-
heuristics,
global
optimization,
machine
learning,
data
mining,
bioinformatic
s,
graph
theory
and
parallel
programming.
He
has
published
over
2
0
papers
in
international
journals
and
conferences.
He
can
be
contacte
d
at
email
:
wa2010
@
bau.edu.jo.
Dr. Ibrahim Mah
moud Alturan
i
is an instruc
tor in the
D
epartmen
t of Co
mputer
Scienc
e
at
Ajloun
College,
Al
-
Balqa
Applied
University,
Jordan.
He
earned
his
B
.
S
.
and
M
.
S
.
degrees
in
computer
science
from
Yarmouk
University,
Jordan
,
in
2004
and
2007,
respectively,
and
completed
his
Ph.D.
in
computer
science
at
t
he
University
Malaysia
Terengganu,
Malaysia,
in
2021.
He
began
his
academic
career
as
a
part
-
time
lecturer
in
the
Department
of
Computer
Science
at
Yarmouk
Universi
ty
from
2007
to
2008
before
joining
Al
-
Balqa
Applied
University
as
an
instructor,
where
he
has
been
teac
hing
since
2008.
He
has
published
several
papers
in
international
journals,
with
research
interests
encompassing
knowledge
representation
through
ontology
and
knowledge
g
ra
phs,
natural
language
processing,
content
-
based
retrieval,
and
artificial
intelligence
.
H
e
ca
n
be
contacted
at
email:
traini111@bau.edu.jo.
Roba
Mahmoud
Ali
Aloglah
received
her
bachelor'
s
degree
o
f
informatio
n
technology
from
Al
-
Balqa
Applied
University
in
2004.
She
received
t
he
master'
s
degree
from
the
Arab
academy
Jordan,
Amman
in
2005.
She
is
a
lecturer
of
computer
science
and
information
technology
at
Department
of
Management
Information
S
cience,
Amman
College
for
Financial
and
Managerial
Sciences,
Al
-
Balqa
Applied
University
,
Amman,
Jordan
since
2008.
Her
research
interests
include
algorithms,
computer
networks,
a
rtificial
intelligence
and
computer
security.
She ca
n be c
ontact
ed at
email:
robaja
bali@bau.edu.
jo.
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