TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4833 ~ 4
8
3
9
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.584
2
4833
Re
cei
v
ed
Jan
uary 5, 2014;
Re
vised Ma
rch 18, 2014; A
c
cepted Ma
rch 29, 2014
Resear
ch on the Public Transport Network Based on
Complex Network
Dan
Wang*,
Beilei Li, Jiay
ang Li, Changto
ng Li, Liy
ong Wan
g
Ke
y
Lab
orator
y of Manufacturi
ng
Industri
a
l In
tegrated A
u
to
mation,
She
n
y
ang U
n
ivers
i
t
y
,
Shen
ya
ng,
110
04
4, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
w
a
ng
da
n03
0
7
@1
26.com
A
b
st
r
a
ct
T
he pu
blic tra
n
s
port infrastruc
ture of a city is
one
of the mo
st imp
o
rtant in
dicators
of its econo
mi
c
grow
th an
d d
e
v
elo
p
m
ent. H
e
re w
e
inv
e
stig
ate the statisti
cal pr
op
erties
of the p
u
b
lic tr
ansp
o
rt netw
o
r
k
in
Sheny
an
g to explor
e its vario
u
s prop
er
ties b
a
sed o
n
co
mpl
e
x netw
o
rk theory.
T
he statistical pro
perti
es o
f
the public transport system cons
ist of the degree
of a node,
th
e av
erag
e sh
ortest
path
le
ngth,
the
clusteri
ng co
efficient of a n
o
d
e
,
the avera
g
e
clusterin
g
coe
fficient, and
th
e degr
ee d
i
stri
butio
n. In contras
t
w
i
th the s
m
all
w
o
rld ev
oluti
o
n
mod
e
l, w
e
fi
n
d
that
the
pu
bli
c
transp
o
rt sys
tem
of S
heny
a
ng, a
n
e
tw
ork of
pub
lic tra
n
sp
or
tation r
outes
c
onn
ected
by
b
u
s li
nks, is
a
s
m
a
ll-w
o
rld
n
e
tw
ork character
i
z
e
d
by
a P
o
is
son
degr
ee
distrib
u
t
ion. Si
mu
lati
o
n
resu
lt
s
show
that
the pub
lic transport netw
o
rk exh
i
bits s
m
all w
o
rl
d b
e
h
a
v
i
or
w
i
th N=
148.
Ke
y
w
ords
: pu
blic trans
port n
e
tw
ork, compl
e
x netw
o
rk, sma
ll-w
o
rld n
e
tw
ork
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Tran
sp
ortatio
n
infrast
r
u
c
tures are of cru
c
ia
l importan
c
e to the dev
elopment of a country.
They su
ppo
rt movement o
f
goods
and
peopl
e acro
ss
the count
ry, thereby driv
ing the natio
nal
eco
nomy [1]. Roa
d
ways,
railways, an
d
airways a
r
e
the majo
r
mean
s of tra
n
sp
ort in
Chi
na.
Und
e
rstandi
n
g
of these tra
n
sp
ortation
systems i
s
imp
o
rtant for rea
s
on
s of poli
c
y, administration
and efficie
n
cy
.
The i
n
tricate
structu
r
e
of
interactio
ns
of
many
nat
ural
an
d
so
ci
al sy
stem
s h
a
s
bee
n
obje
c
t of intense research
in the new a
r
ea of com
p
l
e
x networks. Most of the effort in this area
has
bee
n di
rected to
find
the topolo
g
ical prope
rt
ies of
real wo
rld netwo
rks and
unde
rstand
t
he
effects th
at these p
r
op
erti
es
ca
st o
n
dynam
ical p
r
oce
s
se
s ta
ki
ng pl
ace o
n
these
comp
lex
netwo
rks. F
o
r insta
n
ce, the
small
-
worl
d
cha
r
a
c
teri
stic, whe
r
e
ea
ch
node
of the
n
e
twork i
s
only
a
few
con
n
e
c
tions ap
art fro
m
any oth
e
r,
permits
a q
u
ick
spreadi
n
g
of info
rmat
ion throug
h t
h
e
netwo
rk, bei
n
g
fundame
n
ta
l in processe
s of global co
o
r
dinatio
n and
feedba
ck reg
u
lation [2].
Duri
ng th
e pa
st few ye
ars,
sin
c
e the
exp
l
osio
n of the
compl
e
x net
work
scien
c
e
that ha
s
taken
pla
c
e a
fter wo
rks of
Watts a
nd St
rogat
z [3] as
well a
s
Ba
ra
basi
and Alb
e
rt [4, 5] a lo
t of
real
-world n
e
tworks have b
een examin
e
d
, such as
In
ternet, WWW, world
-
wid
e
airpo
r
t netwo
rk,
comm
utation
netwo
rks, electri
c
net
works, f
ood
web
s
, cell
metaboli
s
m, sci
entific research
coo
peration
relation
s, and
citation n
e
two
r
ks [6
-8]. The
pione
eri
ng
work of
Watts
and Strogat
z
[3]
open
ed
a
co
mpletely ne
w field of
re
se
arch. Its m
a
i
n
contrib
u
tion
wa
s to
sho
w
that ma
ny real-
worl
d net
works
have prop
erties
of ran
dom graph
s
and p
r
op
ertie
s
of re
gula
r
low dim
e
n
s
io
nal
lattices. A m
odel that
co
uld explai
n t
h
is
o
b
serve
d
behavio
r
wa
s mi
ssi
ng a
n
d the p
r
op
osed
”sm
a
ll-wo
rld” model of th
e autho
rs tu
rned the inte
rest of a larg
e numb
e
r of
scie
n
tist in
th
e
statistical me
cha
n
ics
com
m
unity in the
dire
ction of
this ap
pealin
g su
bje
c
t [9]. A model
was
prop
osed for the evolutio
n of weig
hte
d
evolvi
ng n
e
tworks in a
n
effort to understan
d th
e
statistical pro
pertie
s
of re
al-worl
d
syst
ems.
The to
pology of these sy
stems
wa
s found to
be
having sm
all-worl
d network features an
d a
two-regim
e
power-la
w
degree di
strib
u
tion.
De
spite thi
s
,
at the b
eginn
ing little atten
t
ion ha
s
bee
n pai
d to tran
spo
r
tation
ne
tworks-
medium
s a
s
much
impo
rt
ant and
al
so
sha
r
ing
a
s
m
u
ch
complex
stru
cture a
s
t
hose p
r
eviou
s
ly
listed.
Howe
ver, du
ring t
he la
st few year
s seve
ral
p
ubli
c
transport syst
ems have b
een
investigate
d
usin
g variou
s con
c
ept
s of stat
istical phy
sics of co
mpl
e
x networks [10].
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4833 – 4
839
4834
In this pa
per, we have
studied a
part of
data for the publi
c
t
r
an
spo
r
t sy
stem in
Shenyang
an
d we have
a
nalyze
d
thei
r node
s
deg
re
es,
the avera
ge sho
r
test p
a
th
length,
th
e
clu
s
terin
g
co
efficient, the averag
e clu
s
t
e
ring
c
oeffici
ent, and the degree di
strib
u
tion. In contrast
with the
smal
l wo
rld
evolut
ion m
odel,
o
u
r
analysi
s
shows th
at th
e pu
blic tra
n
s
po
rt
system
ha
s
small
-
world n
e
twork featu
r
es an
d ha
s a Poisson di
stri
bution.
2. The Model
of Public Transpor
t Netw
o
r
k
To analyze variou
s p
r
op
erties of the public tra
n
spo
r
t system on
e sho
u
ld sta
r
t with a
definition of a prope
r network top
o
logy.
The i
dea of the spa
c
e L
and P, propo
sed in a ge
n
e
ral
form in
[11]
a
nd u
s
e
d
also
in [12] i
s
presented
at Fig
u
r
e
1. Th
e first
topolo
g
y (sp
a
ce
L
)
con
s
i
s
ts
of node
s
rep
r
ese
n
ting b
u
s,
tramway or
unde
rg
roun
d
stop
s an
d a li
nk b
e
twe
en t
w
o n
ode
s exi
s
ts
if they are co
nse
c
utive sto
p
s
on the rou
t
e. The node
degree k in th
is topolo
g
y is just the numb
e
r
of dire
ction
s
(it is u
s
u
a
lly twice the
num
ber
of
all p
u
b
lic tra
n
sport
system ro
utes) on
e can ta
ke
from a given
node
while th
e distan
ce l e
qual
s to
the total numb
e
r
of stop
s on th
e path from o
n
e
node to an
oth
e
r [10].
Although
nod
es in
the
sp
a
c
e P
are
the
same
a
s
in th
e previou
s
to
pology, he
re
an ed
ge
betwe
en two
node
s mea
n
s that there is a direct
bu
s,
tramway or
unde
rg
roun
d route that lin
ks
them. That i
s
to say, if a
route
A
con
s
i
s
ts of n
ode
s
i
a
(
1,
2
,
,
in
),then in the
space P th
e
nearest n
e
rg
hbors of the
node
1
a
are
23
,,
,
n
aa
a
.
Con
s
e
quently
the node d
egre
e
k
in thi
s
topology is t
he total num
ber of nod
e
s
re
ach
able
usin
g a rout
e and the di
stan
ce can
be
interp
reted a
s
a numbe
r of transfe
rs one
has to
take to get from one
stop to anoth
e
r.
Another ide
a
of map
p
ing
a
structu
r
e
em
bedd
ed i
n
two-dim
e
n
s
iona
l sp
ace into
a
nother,
dimen
s
ionl
ess topology was used, wh
ere a pl
an of
the city roads ha
s bee
n
mapped into
an
informatio
n
city network. I
n
the la
st to
pology
a
roa
d
re
presents a n
ode
and
an inte
rse
c
tion
betwe
en
roa
d
s
- a
n
e
dge,
so th
e n
e
two
r
k
sho
w
s
info
rmation
handli
ng that
ha
s t
o
be
pe
rform
ed
to get oriente
d
in the city [10].
In the p
ape
r,
we
co
nsid
er the
se
cond
to
pol
ogy
(spa
ce P). Su
ch
a
n
several
oth
e
r type
s
of network
s
y
s
t
ems
:
Internet,
railway or
airpo
r
t networks.
(a)
(b)
Figure 1. Explanation of th
e S
pace L
(a) and the sp
ace P (b)
3. Topologic
a
l Analy
s
is o
f
the Public
Transp
ort
Net
w
o
r
k
Deg
r
ee
of a
n
ode i
s
th
e nu
mber of n
ode
s it
i
s
di
re
ctly con
n
e
c
ted to.
De
gre
e
of
a
node
i
is define
d
as:
1
N
ii
j
j
ka
(1)
In a dire
cted
netwo
rk, in
-d
egre
e
(o
ut-d
e
g
ree
)
of a no
de is the
num
ber of in
-comi
ng (o
ut-
going
) lin
ks. In the p
ubli
c
tran
spo
r
t net
work of She
n
yang, in
-de
g
re
e (
in
i
k
) an
d out
-degree
(
ou
t
i
k
)
of the public transport
stand for the
numbe
r of
b
u
s termi
natin
g-into an
d n
u
mbe
r
of bu
s
origin
ating-f
r
o
m
, respe
c
tively. We ob
se
rve that fo
r a
very larg
e nu
mber
of nod
e
s
in th
e pu
bli
c
transpo
rt network
in
o
u
t
ii
kk
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
the Public Transport Network
Ba
se
d on
Com
p
lex Network (Da
n
Wang)
4835
In a network,
the distan
ce
betwe
en two
node
s, label
e
d
i
and
j
respec
tively, is
define
d
as th
e nu
mb
er of
edge
s
along th
e
sh
ortest
path
conne
cting th
e
m
. The ave
r
a
ge sho
r
test
p
a
th
length
L
of the netwo
rk, the
n
, is define
d
as the m
ean
distan
ce b
e
twee
n two n
o
des, ave
r
ag
e
d
over all pai
rs
of node
s.
The ave
r
ag
e sho
r
test p
a
th
length (
L
) for
a dire
cted
ne
twork with
N
n
ode
s is
defin
ed
as:
,1
;
1
(1
)
N
ij
ij
i
j
L
L
NN
(2)
Whe
r
e
ij
L
is the sho
r
test path
length from n
ode
i
to
j
.
In term
s of n
e
twork to
polo
g
y, cluste
rin
g
,
also
kn
own
as tran
sitivity, is a
typical
p
r
ope
rty
of acquai
ntan
ce
networks,
whe
r
e t
w
o
in
dividual
s
with
a
comm
on f
r
iend
are
likel
y to kn
ow ea
ch
other [7]. In term
s of a generi
c
gra
ph
G, transit
ivity means the
pre
s
en
ce of a high numb
e
r of
triangle
s
. Th
e clu
s
teri
ng
coeffici
ent (
i
C
)
of a node i
s
defined a
s
th
e ratio of n
u
m
ber
of links
sha
r
ed
by its neigh
bori
ng n
ode
s to the m
a
ximum num
ber of po
ssibl
e
links amo
n
g them. In other
wor
d
s,
i
C
is the
probability t
hat two
no
de
s a
r
e
lin
ked
to ea
ch
othe
r given
that t
hey a
r
e
both
c
o
nn
ec
te
d
to
i
[13].
There a
r
e
two definitio
ns
of the
clu
s
tering
coeffici
en
t. Here, we a
dopt the
wi
d
e
ly used
definition give
n by Watts an
d Strogatz [3]
.
nu
m
b
e
r
of
tr
ia
ngl
e
s
c
o
n
n
e
c
t
ed
to v
e
r
t
ex
n
u
m
b
e
r
o
f
tr
ip
l
e
s c
e
n
te
r
e
d
on
v
e
r
t
e
x
i
i
c
i
.
(3)
A quantity
i
c
(the local clu
s
tering
coeffici
ent of node
i
) is
firs
t introduc
ed, express
i
ng
how li
kely
1
jm
a
fo
r
tw
o
ne
ig
hb
or
s
j
and
m
of node
i
. Its value is obtai
ned b
y
countin
g the
actual n
u
mb
er of edg
es
(denote
d
by
i
e
) in
i
G
(the sub
g
rap
h
of nei
ghbo
rs of
i
). The lo
cal
clu
s
terin
g
co
efficient is de
fined as the ratio betwee
n
i
e
and
(1
)
ii
kk
, the maximum possibl
e
numbe
r of ed
ges in the n
e
twork
[2]:
,
2
.
(1
)
(
1
)
ij
j
m
mi
jm
i
i
ii
ii
aa
a
e
c
kk
kk
(4)
For ve
rtice
s
with d
egree
0 or 1, fo
r
wh
ich
both
nu
merato
r a
nd
denomi
nato
r
are
ze
ro,
they are defin
ed as
0
i
c
.
Then the
clustering coeffici
ent for
the wh
ole network is the average.
1
1
N
i
i
Cc
c
N
(5)
Whe
r
e
01
i
c
,
01
C
and
i
c
is the clu
s
teri
ng co
efficient
of node
i
.
From th
e ab
o
v
e definition
s
, it can b
e
se
en that
C
is a
measure of t
he relative n
u
mbe
r
of triangl
es,
and i
s
stri
ctly in the inte
rval [0, 1], with the u
ppe
r l
i
mit attained
only for
a ful
l
y
con
n
e
c
ted graph. In a so
cial a
c
qu
aint
ance network, for examp
l
e,
1
C
if everyone in the
netwo
rk kno
w
s ea
ch
oth
e
r. In a
dditio
n
, it
has to
be note
d
tha
t
even thou
g
h
the BA m
odel
su
ccessfully explain
s
t
he scale-f
r
ee na
ture
of
ma
ny netwo
rks, it
has
0
C
and th
u
s
fails to
descri
be net
works with th
e high cl
uste
ring, su
ch a
s
social n
e
two
r
ks.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4833 – 4
839
4836
Here we
onl
y analyzed a
part of data
for the publi
c
tran
sp
ort system in Sh
enyang.
More
over we cho
s
e n
u
mbe
r
s of no
des in
the public tra
n
sp
ort network of Shenyan
g
148
N
.
One shoul
d n
o
tice that oth
e
r
surveys
explorin
g the propertie
s
of tra
n
sp
ortation
n
e
tworks
have u
s
ually
dealt with
smaller
numb
e
rs
of vertice
s
, su
ch
as
N = 76 fo
r U-Bahn net
wo
rk in
Vienna [1
2],
N
= 1
24 i
n
B
o
ston
Unde
rg
roun
d T
r
an
sp
ortation Sy
stem [14]
or
N
= 1
28 i
n
Airp
ort
Network of China [15].
Reg
u
lar lattices
are
cl
uste
red, b
u
t do
n
o
t exhibit the
small
-
worl
d
effect in g
e
n
e
ral. O
n
the other h
a
n
d
, rando
m graph
s sh
ow th
e small
-
worl
d
effect, but do not sho
w
cl
usteri
ng. Thu
s
, it
is n
o
t surpri
sing to
se
e th
at the
reg
u
la
r lattice mo
d
e
l an
d the
E
R
ran
dom
m
odel
both fail
to
rep
r
od
uce so
me importa
nt features of many real
network
s
.
After all, mos
t
of these real
-wo
r
ld
netwo
rks a
r
e
neither
entirely regula
r
n
o
r
entirely r
ando
m. The reality is that pe
opl
e usually kno
w
their nei
ghbo
rs, but thei
r circle of a
c
q
uaintan
ce
s m
a
y not be co
nfined to tho
s
e who live right
next doo
r, as the lattice m
odel
woul
d i
m
ply.
On the
other
han
d, ca
se
s like lin
ks
amo
ng
Web
page
s on the
WWW were certainly not created at ra
n
d
om, as the ER pro
c
e
s
s wo
uld expe
ct [16].
Aiming to
de
scribe
a
tran
sition f
r
om
a
re
gula
r
lattice to a
rand
o
m
graph,
Wa
tts and
Strogatz [3] i
n
trodu
ce
d an
intere
sting
small-worl
d ne
twork mo
del,
referred to
as WS sm
all-world
model. The
WS small
-
wo
rld mod
e
l alg
o
rithm a
s
follows:
1) Start with
orde
r: Begin with a nea
rest
-nei
ghb
or coupl
ed net
work con
s
isti
ng of N
node
s arran
g
ed in a ring, whe
r
e ea
ch n
ode
i
is adjacent to its neighbor n
ode
s,
1,
2
,
,
2
ik
,
with
k
being ev
en.
2)
Ra
ndomi
z
ation: Rand
o
m
ly re
wire e
a
c
h
edg
e
of
th
e net
wo
rk wit
h
p
r
ob
ability
p; varying
p in su
ch a
way that the
transitio
n be
tween o
r
d
e
r
(
0
p
) and ra
ndo
mness (
1
p
) can
be
clo
s
ely monit
o
red.
The
work o
n
WS small-world n
e
two
r
ks has
sta
r
ted
an avala
n
che
of re
sea
r
ch
on ne
w
model
s of
co
mplex networks, in
clu
d
ing
some
vari
a
n
ts of the
WS
model. A typical va
riant
was
the one prop
ose
d
by Newman and
Wat
t
s [17], referred
to as the NW
small
-
wo
rld mod
e
l lately. In
the NW m
o
d
e
l, one
doe
s not b
r
ea
k a
n
y co
nne
ctio
n bet
ween
a
n
y two n
e
a
r
e
s
t nei
ghbo
rs, but
instead, adds with probability p a connection be
tween a pai
r of nodes. Li
kewise, here one does
not allow a n
ode to be cou
p
led to anoth
e
r nod
e more
than once, or to couple
with itself.
With
0
p
, the NW model red
u
ce
s to the original n
earest-neigh
bo
r co
upled net
wo
rk,
and if
1
p
it becomes
a glob
ally coupl
ed
netwo
rk. Th
e
NW mo
del i
s
so
me
what
easi
e
r to
analyze than
the original
WS model becau
se it
does not lea
d
to the formation of isola
t
ed
clu
s
ters, whe
r
ea
s this ca
n indeed h
a
ppen in the WS model. For sufficient
ly small
p
and
s
u
ffic
i
ently large
N
, the NW
model i
s
e
s
se
ntially equival
ent to the WS
model. To
da
y, these two
model
s are together
comm
only termed
sm
all-worl
d m
odel
s for brevity [16].
The WS mo
d
e
l and the NW mod
e
l can
be gen
erate
d
as follows (Fi
gure 2
)
[16].
(a) T
he WS small-worl
d m
odel; (b
) The
NW
small
-
wo
rld mod
e
l
Figure 2. The
Small-wo
rld
Model
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
the Public Transport Network
Ba
se
d on
Com
p
lex Network (Da
n
Wang)
4837
Acco
rdi
ng to
the NW
small-worl
d m
odel with
0.4
,
4
pk
and
148
N
，
t
he
averag
e sh
ortest path leng
th and clu
s
tering co
efficien
t, 1.5215 and
0.4587, re
sp
ectively. Whe
n
the NW sm
all
-
wo
rld m
odel
with
0.2
,
4
pk
and
148
N
，
the avera
ge
sh
ortest p
a
th le
ngth
and cl
uste
rin
g
coeffici
ent, 1.7353 a
nd 0.
2576, re
sp
ect
i
vely.
Small-worl
d netwo
rks a
r
e
characte
ri
ze
d by a
very
small ave
r
ag
e sho
r
test pa
th length
(
L
) and a hig
h
averag
e clu
s
t
e
ring
co
effici
ent (
C
). Shorte
st path len
g
th
from nod
e
i
to
j
,
ij
L
,
is the numb
e
r of bus nee
de
d to be taken
to go from
i
to
j
by the shorte
st route.
We fo
und
th
e average
shorte
st path
length
of th
e pu
blic tran
spo
r
t net
wo
rk to
be
1
.
939
2
L
, which i
s
of the o
r
de
r of th
at of a rando
m network of
same
si
ze
an
d average
de
gree.
The ave
r
ag
e clu
s
terin
g
co
efficient of th
e publi
c
tra
n
s
po
rt network wa
s found t
o
be
0
.
53
85
C
,
whi
c
h i
s
an
o
r
de
r of mag
n
i
t
ude hig
her t
han that
of th
e co
mpa
r
abl
e
rand
om n
e
twork. Th
ese two
prop
ertie
s
i
n
dicate
that th
e pu
blic tra
n
sport
net
work
is
a small-world
network
.
ANI [1] has
als
o
been
foun
d t
o
be
small-world
networks. In pa
rt
icul
ar, ANI ha
s
ave
r
age
sho
r
test
path l
ength
and
clu
s
terin
g
co
efficient, 2.25
93 and 0.6
5
7
4
, resp
ectivel
y
.
Table 1. The
Statistical Pro
pertie
s
of the Variou
s Networks with
N=1
4
8
The statistical properties
the public transport
net
w
o
rk
NW small-w
o
rld net
w
o
rk
w
i
th
p=0.4, k=4
NW small-w
o
rld net
w
o
rk
w
i
th
p=0.2, k=4
the average sho
r
test path
length(L)
1.9392
1.5215
1.7353
the average clustering
coefficient(C)
0.5385
0.4587
0.2576
Table 1
sh
o
w
s th
e stati
s
tical prope
rti
e
s of
the va
riou
s net
wo
rks
with
N=1
48, whi
c
h
con
s
i
s
ts
of th
e pu
blic tran
sport n
e
two
r
k
and
NW
smal
l-wo
rld
net
wo
rk with differe
nt
paramete
r
s.
Our
analy
s
is sh
ows that
while th
e p
u
b
lic tran
spo
r
t network i
s
similar to th
e
ANI [1] in
so
me
asp
e
ct
s, it ha
s differen
c
e
s
in so
me featu
r
es a
s
refle
c
t
ed in its
network pa
ramete
rs.
We find th
at
the publi
c
tra
n
sp
ort net
wo
rk h
a
s
small
-
worl
d net
wo
rk features, in
contrast to
NW
small
-
wo
rld
netwo
rk.
Since th
e pu
blic tran
spo
r
t netwo
rk is
a
sm
all
net
work, we anal
yze
the cum
u
lative
degree
distri
bution. We fi
nd that the
cumul
a
tive
d
egre
e
di
strib
u
tion of the
publi
c
tra
n
sp
ort
netwo
rk foll
o
w
s
a Poisso
n
as seen i
n
F
i
gure
3. As we ca
n se
e fro
m
Figure 4 a
nd Figu
re 5,
th
e
cumul
a
tive degre
e
dist
ribu
tion of the NW
sm
all-worl
d model al
so
follow a Poisson.
Figure 3 sho
w
s typical pl
ots for deg
re
e distri
b
u
tion
in the public transp
o
rt ne
twork of
Shenyang. L
e
t us n
o
tice t
hat the num
b
e
r of no
de
s of
degree
k =
1
is sm
aller
as
comp
ared to t
h
e
number of nodes of
degree k =
2 since k
= 1 nodes are
ends
of transport routes. Still some
node
s
(hu
b
s) ca
n have
a
relatively high
degree va
l
ue (in some
cases above 20) but
the
n
u
mb
er
of su
ch ve
rtices i
s
very
sm
all. Deg
r
ee
di
stribut
io
ns
ob
tained for the
publi
c
tra
n
sp
ort net
work i
s
Poisson di
stri
bution a
s
the NW
small
-
wo
rld mod
e
l is.
Figure 3. Deg
r
ee Di
stri
buti
on in the Publ
ic
Tran
sp
ort Net
w
ork of Shen
yang
Figure 4. Deg
r
ee Di
stri
buti
on in NW Small-
worl
d Net
w
o
r
k with p
=
0.2, k=4an
d N=14
8
0
50
10
0
15
0
0
0.
0
2
0.
0
4
0.
0
6
0.
0
8
k
P(
k)
0
50
10
0
150
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
12
k
P(
k)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4833 – 4
839
4838
Figure 5. Deg
r
ee Di
stri
buti
on in NW Small-
worl
d Net
w
ork with p
=
0.4, k=4
and
N=148
4. Conclusio
n
In this
study
we
have
col
l
ected
and
a
nalyz
e
d
a
pa
rt of data
for the p
ublic transport
netwo
rk in S
henyan
g. Sizes of this network is
N=1
4
8
. Using the
con
c
e
p
t of different netwo
rk
topologi
es
we sho
w
that in the spa
c
e
P, wher
e di
st
ances a
r
e m
easure
d
in n
u
mbe
r
s of pa
ssed
bus/tra
m
way stop
s. Its top
o
logy wa
s fo
und to be
ha
ving small
-
wo
rld net
wo
rk fe
ature
s
. Many
of
our
re
sults a
r
e simil
a
r to
feature
s
ob
se
rved in
othe
r wo
rks
reg
a
rding tran
spo
r
tation net
works:
unde
rg
roun
d,
railway o
r
ai
rline sy
stem
s [1], [
10-11],
[14-15]. All such n
e
two
r
ks tend to sha
r
e
small
-
world p
r
ope
rtie
s.
Ackn
o
w
l
e
dg
ements
This work
was fin
a
n
c
ially
su
ppo
rted
b
y
the You
n
g
Scie
ntists F
und
of the
Nation
al
Natural Scie
n
c
e Fo
und
atio
n of Chin
a (6
1203
152
), t
he Scientific
Rese
arch Fo
un
dation for
Do
ctor
of Liaonin
g
Province of Chin
a (20
1
2
1040
) and th
e Natural Science Foun
d
a
tion of Liao
ning
Province (20
1302
0144
).
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TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
the Public Transport Network
Ba
se
d on
Com
p
lex Network (Da
n
Wang)
4839
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