TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6411 ~ 6416
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.533
1
6411
Re
cei
v
ed
De
cem
ber 1
0
, 2013; Re
vi
sed
April 20, 201
4; Acce
pted
May 9, 201
4
Small-world and Scale-
free Features in Harry Potter
Jun Zhan
g
*, Hai Zhao, Ji
u-qiang Xu, Jin-fa Wan
g
Coll
eg
e of Information Sci
enc
e and En
gi
neer
ing, North
easte
rn Univ
ersit
y
,
Shen
ya
n
g
110
819, Ch
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zhang
ju
n1@
i
s
e.neu.e
du.cn
A
b
st
r
a
ct
Harry Potter is
a series
of se
ven fantasy
no
vels
w
h
ich
has
got a h
u
g
e
su
ccess. T
o
expl
ore th
e
reaso
n
s of so successful of the nov
el b
ehi
n
d
, w
e
analy
z
e
d
the characters
netw
o
rk in Har
r
y Potter from the
perspective of complex networks. St
udies sh
ow
that the characters net
work in Harry Potter has got the
sma
ll-w
o
rld
effect and sca
le-
f
ree feature. It is a
typical c
o
mpl
e
x netw
o
rk. T
he success of novel H
a
r
r
y
Potter is prec
is
ely d
ue to the
compl
e
x pro
p
e
r
ties of it, and
this may giv
e
s
o
me g
u
id
anc
e
for nove
l
w
r
iters
w
hen prep
ari
n
g their w
o
rks.
Ke
y
w
ords
: com
p
lex networks, sm
all-world, sca
le-free, rich–club, Harry Potter
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
A netwo
rk i
s
a
set of ite
m
s,
which
we called
vert
ice
s
o
r
n
ode
s, with
conn
ection
s
betwe
en the
m
, called e
d
g
e
s o
r
links. Systems ta
kin
g
the form of netwo
rks ab
o
und in the wo
rld.
For exam
ple,
the Internet is a network o
f
rout
ers or d
o
main
s. The
Wo
rld Wi
de
Web
(WWW) is a
netwo
rk of
website
s
. The
interpe
r
son
a
l network
i
s
constructe
d b
y
the pattern
s of friend
shi
p
s
betwe
en indi
viduals. Th
e
sci
entific
citation network
i
s
a net
wo
rk
of citation
s b
e
twee
n acad
emic
pape
rs. T
he
colla
boration
netwo
rk i
s
a
netwo
rk i
n
which
parti
cipa
nts collab
o
rat
e
in group
s
of
one
kind
or a
nother. T
he b
r
ain i
s
a
network of ne
uro
n
s
. An organi
zation is
a net
work of
peo
ple.
Food
web
s
a
nd metab
o
lic
pathways
ca
n all be
re
p
r
e
s
ente
d
by net
works, and
e
v
en a lan
gua
ge
can
also be
rega
rd
ed a
s
a network which i
s
con
s
t
r
ucte
d by the
words
and t
he rel
a
tion
shi
p
s
among the
m
.
Over the pa
st few years, complex networks
have
received many a
ttentions from
a wid
e
rang
e of exp
e
rts i
n
vari
o
u
s field
s
and
have
b
een i
n
tensively
studied
acro
ss many field
s
of
sci
en
ce. A wide ra
nge of
real
worl
d ne
tworks, from
the Internet [
1
, 2], WWW
[3, 4] to email
comm
uni
cati
ons [5, 6], from large po
wer networ
ks [
7
] to the global transportat
i
on netwo
rks
[8
-
11], from th
e
org
ani
sm i
n
the b
r
ain
[1
2], the p
r
otei
n interactio
n
netwo
rks [1
3] to a va
riety
of
metaboli
c
ne
tworks [1
4, 15], from the sci
entific
coll
aboration net
work [16
-
18]
to a variety of
eco
nomi
c
[19
], from the
supply
chai
n
netwo
rk [
20]
to food
we
bs [21-23], fro
m
the
se
ma
nti
c
netwo
rks [24]
to the software n
e
two
r
ks [25-27], et
c.,
can all b
e
st
udied from th
e persp
ective
o
f
compl
e
x net
works. It wa
s foun
d that
althoug
h
these
networks are from
different a
r
e
a
s,
rep
r
e
s
entin
g different syst
ems, but
all h
a
ve
a si
mila
r
small
-
world
a
nd
scale-f
r
ee
feature
s
. It
can
be foun
d that compl
e
x net
work the
o
ry h
a
s b
e
come
a
powerful tool
to analyze the stru
ctu
r
e a
s
a
whol
e and its
dynamical propertie
s
of
variou
s types of
complex sy
st
ems.
The n
o
vel is
a refle
c
tion
o
f
the re
al world. The
ch
ara
c
ters n
e
two
r
k in a
novel i
s
simila
r
with the interperson
a
l net
work of
the real wo
rld. To
explore the
reason
s of the succe
s
s of n
o
vel
Harry Potter, we analyze
d the cha
r
a
c
ters network
in it from the perspe
c
tive of com
p
lex
netwo
rks.
2. Extrac
tion
of the Chara
c
ter
s
Ne
t
w
o
r
k in Harr
y
Potter
Harry Potter [
28] is a
seri
e
s
of
seven fa
ntasy
no
ve
ls
w
r
itte
n b
y
th
e Br
itis
h au
th
or
J
.
K.
Ro
wling. Sin
c
e the relea
s
e of the first novel
“Harry Potter and th
e Philoso
phe
r's Ston
e” on
30
Jun
e
1
997,
the bo
oks
h
a
ve gai
ned
i
mmen
s
e
pop
ularity, critical a
ccl
aim a
nd
comm
erci
al
su
ccess
wo
rldwid
e. As of
Jun
e
20
11, th
e boo
k
se
rie
s
has
sol
d
ab
o
u
t 450 milli
on
copi
es, m
a
ki
ng
it the best-sel
ling boo
k seri
es in hi
story,
and ha
s be
en
translate
d into 67 lang
uag
es [29].
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 641
1 –
6416
6412
The
cha
r
a
c
te
rs net
work i
n
Ha
rry P
o
tter is
co
nst
r
u
c
te
d by the
pe
rsons ap
pea
re
d in th
e
novel and th
e relatio
n
ship
s amo
ng the
m
. We choo
se the pe
rson
s except gobl
ins, hou
se
-el
v
es
and g
h
o
s
ts a
ppea
red i
n
th
e novel a
s
no
des
and ta
ke
the relatio
n
ships
between
the perso
ns
a
s
links
to cons
truc
t the charac
ters
network
. If two
pe
rsons
are
frien
d
s o
r
they h
a
v
e com
bated
face
to face in on
e battle, there is a lin
k bet
wee
n
them. In ord
e
r to ob
tain a co
nne
cted netwo
rk, the
cha
r
a
c
ters n
e
twork
doe
s
not contain t
he pe
rs
on
s
once ap
pea
red in th
e no
vel but have
n
o
conta
c
t with
t
he
oth
e
r
characters, su
ch
as so
me
f
r
e
s
hmen
mentio
ned i
n
the
So
rting
Hat
and
the
players of Bulgari
an Q
u
i
dditch tea
m
and Iri
s
h Q
u
idditch tea
m
in Quiddit
c
h
Wo
rld Cup,
etc.
Finally we got
a network wit
h
317 no
de
s and 11
46 lin
ks.
3. The Small
-
w
o
rld Effect in Harr
y
Potter
The
small
-
wo
rld effe
ct i
s
o
ne of th
e
sign
ificant
re
cent
discoveri
e
s in
the field
of
complex
netwo
rks. In 1998, D. J.
Watts an
d his advisor S. H. Strogatz in
the Co
rnell
University of United
States pu
blished a
pap
er entitled
“Col
lective dyna
mics of ‘sm
a
ll-wo
rld’
networks” in
Natu
re,
revealin
g the
small
-
worl
d
feature
sh
are
d
by m
any
real-wo
r
ld n
e
tworks [30]. B
y
saying
sm
all-
worl
d, it me
a
n
s th
e n
e
two
r
k
ha
s
small
averag
e p
a
th
length
and
l
a
rge
cl
uste
rin
g
coefficie
n
t. So
we analy
z
ed the
average
path
le
ngth a
nd clu
s
terin
g
co
efficient
o
f
the Charact
e
rs Netwo
r
k i
n
Harry Potter.
We first com
puted the
averag
e path
le
ngth of
the
chara
c
te
rs
net
work i
n
Harry Potter,
whi
c
h i
s
2.73
99. It is sm
all
comp
ared
wi
th the tota
l nu
mber
of the n
ode
s in the
n
e
twork. Th
e two
main
ch
ara
c
t
e
rs in
the
n
o
vel a
r
e
Ha
rry Potter
an
d Lo
rd
Volde
m
ort. Th
e
st
ory i
s
exp
a
n
ded
arou
nd them
. Most chara
c
ters of the netwo
rk
can
be found throug
h Ha
rry Potter or Lord
Voldemo
r
t wh
ich re
sult
s in the small ave
r
age path le
ng
th of the network.
On the
oth
e
r han
d,
we
a
l
so
co
mpute
d
the
cl
uste
ring
coeffici
en
t of the
ch
a
r
acte
rs
netwo
rk i
n
Harry Potter, which i
s
0.413
2. In the
novel of Harry Potter, the mai
n
cha
r
a
c
ters
are
Harry Potter and Lo
rd Vol
demo
r
t. The other char
act
e
rs a
r
e a
rra
n
ged aroun
d them. The frie
nds
of Harry are friend
s of each other, and the Death
Eat
e
rs a
r
ou
nd L
o
rd Volde
m
ort are familiar wit
h
each other. S
o
the clu
s
teri
ng co
efficient
of the
characters net
wo
rk i
n
Harry Potter is high.
In s
u
mmary, the c
h
arac
ters
network
in
Ha
rry Potter
has
small av
erag
e path le
ngth and
large
clu
s
teri
ng co
efficient
. So it is a small-
worl
d ne
twork whi
c
h
made the no
vel plot comp
act
and spellbin
di
ng. It laid the
foundatio
n for the succe
s
s of novel Harry Potter.
4. The Scale-free Fe
atu
r
e
of the
Char
a
c
ter
s
Ne
t
w
o
r
k in Harr
y
Potter
Another si
gni
ficant recent
discovery i
n
t
he
field
of co
mplex net
works is the o
b
servation
that many large-scale com
p
lex
netwo
rks are
scale
-
free. In 1999,
Professo
r A. L. Barabá
si a
nd
his Ph. D
st
udent R. Alb
e
rt publi
s
h
e
d
a pape
r
en
titled “Emerg
ence of scali
ng in rando
m
netwo
rks” in
Scien
c
e, reve
aling the
scal
e-fre
e
feature
sha
r
ed by m
any r
eal
-worl
d
netwo
rks [3
1].
By saying
scale-free, it m
ean
s the
de
g
r
ee
of
n
ode
s obey
s th
e p
o
we
r-l
aw de
g
r
ee
di
stributio
n.
That is mo
st node
s have v
e
ry few links
and yet a few node
s have
many links.
We
analyzed
the de
gre
e
d
i
stributio
n of t
he
cha
r
a
c
ters netwo
rk in
Harry Potte
r, which i
s
sho
w
n
in Fi
g
u
re
1. It ca
n
be
see
n
that t
he d
egree
distribution
of th
e charac
te
r
s
netwo
rk
in H
a
rry
Potter satisfie
d power-la
w
. The expon
ent
of the distrib
u
tion is 1.28
3
5
.
The bo
oks of
Harry Potter chroni
cle th
e adventu
r
e
s
of a wiza
rd,
Harry Potter, and hi
s
friend
s Ronal
d We
asl
e
y a
nd Hermi
one
Gran
ge
r,
all of whom
are stude
nt
s at
Hogwarts S
c
h
o
o
l
of Witch
c
raft and Wi
za
rdry
. The main story arc co
n
c
ern
s
Ha
rry'
s
que
st to overcome the
Da
rk
wizard
Lord
Voldemo
r
t, whose aim
s
a
r
e to be
co
m
e
immortal, con
que
r
the wizardi
ng wo
rld,
subj
ugate n
o
n
-ma
g
ical pe
ople, and d
e
s
troy all tho
s
e who
stand
in his way,
esp
e
ci
ally Ha
rry
Potter.
The first five
node
s that
ha
ve got the
big
gest
deg
ree
in the
cha
r
a
c
t
e
rs net
work i
n
Harry
Potter are
Harry Potte
r, Ron
a
ld
Wea
s
ley, Albu
s
Dumbl
edo
re,
He
rmion
e
Gran
ge
r an
d
Lord
Voldemo
r
t re
spe
c
tively. Harry Potte
r a
nd Lo
rd
Vold
emort
are
two main
chara
c
ters in
the n
o
vel.
Ron
a
ld
Wea
s
ley and
He
rmione
Gra
n
g
e
r a
r
e
Ha
rry’
s
be
st frie
nd
s. They tog
e
ther
com
p
lete
d a
numbe
r of ta
sks
su
ccessf
ully. Albus Dumbled
o
re
is the hea
rt an
d so
ul of the
novel, links
the
past an
d no
w of Hogwart
s
School. Th
ey have a la
rg
e
of followers. Lord Vol
dem
ort is the lea
d
e
r
of Death
Eaters.
He
ha
s
also
got a l
a
rge of fo
llo
we
rs. So th
ey h
a
ve got a l
a
rge of lin
ks,
a
nd
most of th
e o
t
her p
e
rso
n
s
in the n
o
vel a
r
e a
r
rang
ed f
o
r the
m
, so t
hey only h
a
ve got
a few li
nks
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Sm
all-worl
d a
nd Scale
-
fre
e
Featur
es
in
H
a
rry
Potter
(J
un Zhang)
6413
that leadi
ng t
o
the
po
we
r-l
aw
deg
ree
di
stributio
n.
An
d this ma
de
the mai
n
cha
r
acte
rs in
th
e
novel pro
m
in
ent and di
stin
ctive.
(a) the d
egre
e
distrib
u
tion
(b) the fi
tne
s
s of figure (a
) unde
r the log
a
rithm
c
o
or
d
i
na
te
s
Figure 1. The
Degree Di
stri
bution of t
he Charac
ters
Networ
k
in Harry Potter
5. The Othe
r Propertie
s o
f
the
Char
acters Ne
t
w
o
r
k
in Harr
y
Potter
5.1. Degre
e
Correla
tion
Deg
r
ee
co
rre
lation of a network
can b
e
described
by the avera
ge deg
ree of
neare
s
t
neigh
bors. T
he ave
r
ag
e
degree
of ne
are
s
t
nei
ghb
ors of the
n
ode
s with
de
gree
d
,
d
nn
(
d
), is
defined a
s
fol
l
owe
d
[32]:
)
(
/
1
1
)
(
j
V
i
i
d
d
j
j
d
nn
d
d
n
d
d
j
(1)
Whe
r
e
V
(
j
) i
s
the set of th
e neigh
bo
r n
ode
s
d
j
of no
de
j
,
n
d
is th
e numb
e
r of
the nod
es
wi
th
degree
d
.
If
d
nn
(
d
) in
creases with
d
, the net
work i
s
a
n
a
s
so
rtativ
e netwo
rk,
otherwi
se
it is
a
disa
ssortative
network.
The average
degre
e
of neare
s
t nei
g
h
bors of the node
s with de
gree
d
,
d
nn
(
d
), in the
c
h
arac
ters
network
in Harry Po
tter is describe
d
as Fi
gure 2.
Figure 2. Average
Nea
r
e
s
t Neig
hbo
rs a
s
a Function
of
the Degree o
f
the Chara
c
t
e
rs
Network i
n
H
a
rr
y Potter
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 641
1 –
6416
6414
The
ave
r
a
ge degree of
ne
are
s
t
nei
ghb
o
r
s of
the nod
es with
d
e
g
r
e
e
d
,
d
nn
(
d
),
d
e
cr
ea
se
s
with deg
ree
d
from the whole in the chara
c
te
rs net
wo
rk in Harry Potter which
means that the
netwo
rk is a
disa
ssortative
network, that
is th
e
n
ode
s
with lo
we
r d
e
g
ree
tend
to
conne
ct
with t
he
node
s with hi
gher d
e
g
r
ee.
There are
on
ly a few main
roles in th
e novel
. The m
o
st pe
rsons
are
supp
ortin
g
role
s.
They are fam
iliar
with
Harry Potter, Albus
Dum
b
ledore, or Lord Voldemort. So the nodes
with
lowe
r deg
re
e
likely to con
nect with th
e
node
s with
highe
r deg
re
e, and the
most nei
ghb
ors’
degree
of the nod
es with
high
deg
ree
are
lower.
Thus lea
d
s t
o
the di
sa
ssortativity of the
netwo
rk.
The
arran
geme
n
t of the
ch
ara
c
ters in
the
n
o
vel mad
e
th
e main
role
s
promi
nent
an
d
the plot compact. Thus enhance
the readability of the
novel.
5.2. The Ric
h
-club Fe
atu
r
e of th
e Cha
r
acters Net
w
ork in Harr
y
Potter
The ri
ch
–cl
u
b phe
nome
n
on me
an
s th
at the ri
ch
n
ode
s, whi
c
h
are
a small
numbe
r of
node
s
with l
a
rge
nu
mbe
r
s of
links,
are very
well
conne
cted
to
each oth
e
r.
The
rich–
c
lu
b i
s
c
h
ar
ac
te
r
i
z
ed b
y
th
e r
i
c
h
–c
lu
b co
n
n
e
c
tivity w
h
ich
m
easure
s
the i
n
terconn
ectio
n
bet
wee
n
ri
ch
node
s.
The ri
ch
–cl
u
b co
nne
ctivity is define
d
as
the
ratio
betwe
en the
numbe
r of l
i
nks that
actually exi
s
t amon
g the
first
r
pe
rcent
nod
es
with t
he big
g
e
s
t d
egre
e
a
nd th
e total po
ssi
b
le
numbe
r amo
ng them, nam
ely,
)
1
)
(
)(
(
))
(
(
2
)
(
r
n
r
n
r
n
E
r
(2)
Whe
r
e
n
(
r
) is the numbe
r
of the first
r
percent
n
ode
s,
E
(
n
(
r
)) is t
he num
ber
o
f
the links th
at
actually exist
among
n
(
r
) n
ode
s.
F
i
g
u
r
e
3
s
h
ow
s th
e r
i
c
h
–c
lu
b co
e
ffic
i
en
t
φ
(
r
) ag
ain
s
t pe
rcenta
g
e
r
of th
e
ch
ara
c
ters
netwo
rk in
Harry Potte
r. It sho
w
s that
the ri
c
h
n
o
d
e
s
o
f
th
e ne
tw
o
r
k
ver
y
w
e
ll
c
o
nn
ec
te
d
betwe
en ea
ch other. Th
e top 1%, 5% and 10% ri
ch
node
s have 1
00%, 81.9% and 55.3% of
the
maximum po
ssi
ble num
be
r of links sep
a
rately.
Figure 3. Rich–cl
ub Conn
ectivity
φ
(
r
) A
gain
s
t Percen
tage
r
of the Cha
r
a
c
ters
Network
in Harry
Potter
The ri
ch no
d
e
s in the n
e
twork a
r
e the
main c
haract
e
rs i
n
the no
vel, most of them are
familiar with e
a
ch oth
e
r, an
d this re
sults i
n
the rich
-clu
b phen
omen
o
n
.
The othe
r pro
pertie
s
of the cha
r
a
c
ters ne
tw
ork in Ha
rry Potter are listed in Tabl
e 1.
Table 1. The
Prope
rties of
the Cha
r
a
c
ters Net
w
ork in
Harry Potter
Max deg
ree
Average degr
ee
Coreness
Di
ameter
Assortative
coefficient
153 7.2303
12
7
-0.2654
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Sm
all-worl
d a
nd Scale
-
fre
e
Featur
es
in
H
a
rry
Potter
(J
un Zhang)
6415
6. Conclusio
n
Studies
sh
ow that the com
p
lex network
doe
s not
o
n
l
y
exist in the
real
wo
rld, b
u
t also
exist in the vi
rtual
worl
d. By anal
yzin
g the characte
rs netwo
rk in n
o
vel Ha
rry Po
tter, we find it
is
a typical
com
p
lex network.
There i
s
the
small
-
worl
d
e
ffect and
scal
e-fre
e
featu
r
e
in it. It has g
o
t
the sam
e
pro
pertie
s
with t
he mo
st com
p
lex netwo
rks in the
real
worl
d. Althou
gh the cha
r
a
c
ters
in the novel
are n
u
me
rou
s
, but the m
a
in char
acte
rs are out
sta
nding,
they have
distin
cti
v
e
person
a
lity. All plots are ex
pand
ed a
r
o
u
nd them.
The
s
e
re
sult in
th
e sm
all ave
r
a
ge p
a
th len
g
th
and l
a
rg
e
cl
usteri
ng
coef
ficient. Th
e
main
ch
ara
c
t
e
rs all
have
a nu
mbe
r
of
followers
which
results in the
scal
e
-free fe
ature. The
co
mplex net
wo
rk pro
p
e
r
ties
of the characters net
wo
rk
in
the novel m
ade the
ch
a
r
acte
rs vivid and vigo
rou
s
, the plot t
h
riving a
nd
spell
b
indin
g
and
captu
r
ed the
imaginatio
n o
f
millions of reade
rs,
youn
g and old, a
c
ross the glo
b
e and create
d
a
mira
cle in the
history of pu
blishi
ng. It is
the comp
l
e
x prop
ertie
s
of the cha
r
a
c
ters network in the
novel com
b
in
ed with the ingeni
ou
s ide
a
s, rich im
agi
nation and fl
exibility of
writing of the writer
made the nov
el got huge
succe
ss.
Wheth
e
r e
a
ch su
cce
ssful
novel ha
s th
e com
p
lex p
r
opertie
s
?
Thi
s
ne
ed
s u
s
to furthe
r
study. If it is true, it will giv
e
guida
nce fo
r t
he
novel writers whe
n
prepar
i
ng thei
r
works, and
can
also h
e
lp pu
b
lishe
rs to de
ci
de wh
ether a
novel ca
n bri
ng them the b
enefit or not.
Referen
ces
[1]
Z
hang J, Z
hao
H, Yang B. F
r
actals on IPv6 n
e
t
w
o
r
k topo
lo
g
y
.
Te
l
k
om
ni
ka
.
201
3; 11(2): 57
7-58
2.
[2]
Yang B, Z
h
a
o
H, Z
hang J, Ai
J, Jia SY, Ge
X, Li
u W
.
Ana
l
y
s
is of interl
a
y
er conn
ectio
n
catastroph
e
characteristics in Inte
rnet AS level topology
.
Te
lkom
n
i
ka
. 20
13; 11(2): 56
7
-
576.
[3]
Adamic LA, H
uberm
an BA. Po
w
e
r-
La
w
D
i
s
tributio
n of th
e W
o
rld W
i
d
e
W
eb.
Scienc
e
. 200
0; 287:
211
5a.
[4]
Albert R, Jeon
g H, Barabás
i A-
L. Diameter
of the
w
o
rld-
w
i
de
w
e
b.
Nature
. 1999; 40
1: 13
0-13
1.
[5]
Ebel H, Mielsc
h L-I, Bornhol
dt S.
Scale-free topol
og
y of
e-mail n
e
t
w
ork
s
.
Phys. Rev.
E
. 2002; 66
:
035
10
3.
[6]
Ne
w
m
an MEJ,
Forrest S, Balthrop J. Emai
l n
e
t
w
o
r
ks
and
th
e spr
ead
of c
o
mputer vir
u
ses
.
Phys. Rev.
E
. 2002; 66: 03
510
1.
[7]
Cotill
a-Sa
nche
z E, Hines PD
H, Barro
w
s
C,
Bl
umsack S.
Comp
arin
g the
T
opologic
a
l a
nd El
ectrica
l
Structure of the North Amer
i
c
an
Electric Po
w
e
r Infrastructure.
IEEE System
s Journal
. 201
2; 6 (4):
616-
626.
[8]
Guimerà R, Mossa S,
T
u
rtschi A, Amaral LAN.
T
he
W
o
rldw
ide Air
T
r
ansportatio
n
Netw
ork:
Ano
m
a
l
ous
Ce
ntrality, Co
mmunity St
ructure
,
and Citi
e
s
’
G
l
ob
al R
o
les
. Pr
oc. Natl. Acad.
Sci. USA.
200
5; 102: 77
9
4
-77
99.
[9]
Li W, Cai X
.
Statistical Anal
ys
is of Airport Ne
t
w
ork of C
h
in
a.
Physical Review E
. 2004; 68
: 46106.
[10]
Latora V, Marc
hiori M. Is the
Boston sub
w
a
y
a small-
w
o
r
l
d
net
w
o
rk
?.
Physica A
. 2002; 3
14: 109-
11
3.
[11]
Rui YK, Ba
n
YF
, W
ang JC, Haas J. E
x
p
l
orin
g
the
patte
rns an
d ev
olut
ion
of self-or
g
aniz
ed ur
ba
n
street net
w
o
rks
through mo
de
l
i
ng.
Euro
pe
an
Physica
l Journ
a
l B
. 2013; 8
6
(3): 3023
5.
[12]
Sporns O. Netw
o
r
k Ana
l
ysis, Compl
e
xit
y
, an
d Brain F
uncti
o
n
.
Compl
e
xity
. 200
2; 8 (1): 56
-60.
[13]
Maslov S, Sn
e
ppe
n K.
Spec
ificit
y
an
d stabi
li
t
y
in t
opo
lo
g
y
of protei
n n
e
t
w
orks.
Scienc
e
. 200
2; 29
6:
910-
913.
[14]
Jeon
g H, T
o
mbor B, Alb
e
rt
R, Oltvai Z
N
, Ba
rab
á
si A-L.
T
he Large-Sc
a
l
e Orga
nizati
o
n
of Meta
bol
ic
Net
w
orks.
Nat
u
re
. 200
0; 407:
651-6
54.
[15]
Silva B
B
M, Mir
and
a JGV, Co
rso G, Cop
e
l
li
M, Vasconc
elo
s
N, Ri
beir
o
S,
Andr
ade
RF
S
.
Statistical
character
i
zatio
n
of an ens
emble
of functio
n
a
l ne
ural n
e
t
w
orks.
European Physical Journal B
. 201
2;
85 (10): 30
48
1.
[16]
Ne
w
m
a
n
MEJ.
Scientific c
o
l
l
abor
ation
net
w
o
r
ks: I. Net
w
o
r
k constructio
n
and
fund
ame
n
tal res
u
lts.
Phys. Rev. E
.
200
1; 64: 016
1
31.
[17]
Ne
w
m
an MEJ.
Scientific coll
aboration
net
w
o
rks: II. Shortest
paths,
w
e
ighted net
w
o
rks,
and centralit
y
.
Phys. Rev. E
.
200
1; 64: 016
1
32.
[18]
Ne
w
m
a
n
MEJ.
T
he structure of scientific
col
l
ab
oratio
n net
w
o
rks
. Proc. N
a
tl. Acad. Sci. USA. 2001
;
98: 404-
40
9.
[19]
Serran
o
MA, Bogu
na M. T
opolog
y of the W
o
r
l
d T
r
ade W
eb.
Phys. Rev. E
.
200
3; 68: 015
1
01.
[20]
F
u
PH, Liu Y
C
. T
he Security An
al
ys
is of
Supp
l
y
Ch
ai
n Net
w
ork B
a
se
d on th
e Com
p
le
x N
e
t
w
ork
.
Advanc
ed Mat
e
rials R
e
se
arc
h
. 2010; 1
43-1
44 (2): 121
8-1
222.
[21]
Camac
ho J, G
u
imerµ
a
R, Am
aral
LA
N. R
o
b
u
st patterns
in
food
w
e
b
struc
t
ure.
Phys. Rev. Lett
. 200
2;
88: 228
10
2.
[22]
Dun
ne JA, W
illi
ams RJ, M
a
rtinez
ND.
F
ood-w
e
b
struc
t
ure a
nd
net
w
o
rk theory:
T
he rol
e
of
conn
ectanc
e a
nd si
z
e
. Proc. Natl. Acad. Sci
.
USA. 2002; 9
9
: 1291
7-1
292
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 641
1 –
6416
6416
[23]
Dun
ne JA, W
illi
ams RJ, Martinez N
D
. N
e
t
w
o
r
k structu
r
e and
bi
odiv
e
rsit
y
loss i
n
food
w
e
bs:
Rob
u
stness in
creases
w
i
t
h
conn
ectanc
e.
Ecolo
g
y Letters
. 200
2; 5: 558-5
67.
[24]
Ste
y
v
e
rs M, T
enen
ba
um JB.
T
he large-sc
al
e structure
of
s
e
mantic
net
w
o
r
ks: St
atistical a
nal
ys
es a
nd
a mode
l for semantic gro
w
t
h
.
Cog
n
itive Sci
e
nce
. 200
5; 29: 41-7
8
.
[25]
Xu JQ, Li
u H,
Z
hao H, Yu
S. Researc
h
o
n
Structural H
o
les and Clos
eness of
Softw
a
r
e
N
e
t
w
ork.
Journ
a
l of Nort
heaster
n
Univ
e
r
sity
. 2010; 31
(11): 156
2-1
5
6
5
.
[26]
Li P, Z
hao
H, L
i
u Z
,
Li H. Soft
w
a
re
net
w
o
rk
eig
enva
l
u
e
bas
ed o
n
the c
o
re
inh
e
ritanc
e tre
e
.
Journ
a
l of
Northe
astern U
n
iversity
. 20
11;
32 (3): 368-3
7
1
.
[27]
Z
heng
XL, Z
e
n
g
D, Li HQ, Wang F
Y
. Anal
yzing o
pen-s
our
ce soft
w
a
r
e
s
y
stems as comple
x net
w
o
rks.
Physica A
. 20
0
8
; 387 (24): 6
1
90-6
200.
[28]
Ro
w
l
in
g
JK.
Ed
i
t
o
r
s
.
T
he C
o
mplete
Harr
y
Potter Co
llecti
on (S
ign
a
ture
Editio
n). L
ond
o
n
: Blo
o
msb
u
r
y
Publ
ishi
ng PL
C. 2010.
[29]
W
i
kiped
ia. http
://en.
w
i
ki
pe
dia.
org/
w
i
ki/H
arr
y
_
P
otter. 2013.
[30]
W
a
tts DJ, Strogatz SH. Coll
e
c
tive
d
y
nam
ics
of ‘small-
w
o
r
l
d
’
net
w
o
rks.
Nat
u
re
. 199
8; 393:
440-4
42.
[31]
Barab
á
si AL, A
l
bert R. Emerg
ence of scal
i
n
g
in rand
om net
w
o
rks.
Scienc
e
. 1999; 28
6: 50
9-51
2.
[32]
Pastor-Satorra
s R, Váz
q
u
e
z
A, Vespi
g
n
ani
A.
D
y
nam
ical
and
corre
lati
on
pro
perties
of t
he Inter
net.
Phys. Rev. Lett
. 2001; 87: 25
8
701.
Evaluation Warning : The document was created with Spire.PDF for Python.