How Close a Bataknese One Another?
Study of Indonesian Batak’s Family Tree
Hokky Situngkir
Dept. Computational Sociology
Bandung Fe Institute – Indonesia
The paper conjectures some alternative acquisitions of mathematical models to see the Batak family
tree that could enrich our understanding of the anthropological study of Bataknese people. We
discuss some aspects of Bataknese Clan‐group in Batak traditional social life. Since the family tree is
drawn according to the genealogical patterns of degrees relative to the first Batak in northern
Sumatera, the paper discusses interesting features of Malthusian growth rate. The latter discussions
is about the relatedness of a clan‐group of Bataknese one another as reflected in the family tree by
observing the topology of the web. The conjectures for future development is also drawn.
Keywords: family tree, batak, customary law, scale‐free network.
1. Introd
their gro
and amo
lot of int
of the c
early ge
There a
among t
clan gro
but diffe
More than t
ese is sprea
rated in the
trated in n
trated in sou
oup of clan.
ong Batakne
teresting thi
community o
enealogy of B
re about six
ling, Pakpak,
these ethnic
e until now
oups (Sinaga,
erent theore
ures of family
the populatio
ten millions
ading over t
e large island
north), Nias
uth) since the
Batak peopl
The study re
ese when the
ngs that we
of Indonesia
Bataknese h
x ethnicities
, Simalungun
c groups alo
s, an interes
and still tod
, 1997). An
etical conjec
y trees relate
he cartogram s
on fraction of
the archipe
d of Sumate
s (concentra
e very first id
le are well k
egarding to t
ey are talking
can learn fr
Batak peop
habited the n
can be rega
n, and Angko
ng with oth
sting thing i
day a lot of d
interesting a
ctures is disc
ed to the DN
showing the 3
Batak ethnic
people is in
lago as sho
era neighbor
ated in NIa
dentified as
known for k
this issue mo
g about trad
om this trad
ple even toda
northern Sum
arded as Bat
ola. The stat
er ethnic gr
in Bataknese
debates are
and similar d
cussed in Bo
NA is discusse
Figure 1
30 regions in I
group. The lig
the set of B
own in Figu
ring and livin
as Island i
Batak people
keeping their
ostly become
itional socia
ditional custo
ay. Batak’s c
matera at th
taknese, i.e.
tistical proxim
oups in Indo
e is that the
going on re
data used re
ouquet (199
ed in Serva (
ndonesia resi
ghter the colo
dung s
dung marsu
Batak ethnic
ure 1 while
ng closely w
n the East
e until now.
r “marga”, a
es the discou
l law (‘adat’
oms and how
clan groups
he place kno
: Batak Toba
mities of the
onesia are d
ey keep usin
egarding to t
elated to soc
96) while som
zed regarding
or the more Ba
sansimu mar
uhu‐suhu ma
groups. The
most of th
ith Malay, A
t), and Pad
surname r
urse of anth
’). In fact, the
w it emerges
are rooted f
own as the T
a, Batak Kar
e different la
discussed in
ng the usag
the genealog
ciological dis
me biologica
g to
ataknese in it.
e modern
hem are
ere are a
the face
from the
ro, Batak
ge of the
gy of the
al theory
The wor
the maj
from the
one ano
2. Abou
the num
using th
all Batak
clan gro
noting t
to be co
the diffe
rk presented
nal Indonesi
tive in Situng
or role of t
to this aspe
e genealogy
other conce
ese as well as
t Bataknese
Even furthe
mber of the
er the label “
e same word
k people as h
ups, while th
hat the gene
ounted on in
ng polygamy
as the same
ndong’) is re
erent social p
d here show
ian culture –
gkir (2003 &
he clan gro
ect and then
of the clans
rning their
s a lot more f
and its Clan
r, they also
“sundut” –
king” here
d (“raja”) as
his descenda
he surname
ealogy depic
n the constr
y or married
e. Consequen
ecognized to
positions bet
s some insig
as it has
2004) – esp
up among I
followed by
s and thus fo
clan groups
from the div
have some
degree from
cannot be r
s for political
ants (cf. Sina
(the “marga
cted here is
uction of cla
d other wom
ntly to the p
be the part
tween male a
A Chart Dep
ghts that we
been theor
pecially Bata
ndonesian B
y some discu
ollowed by th
s. A lot of t
verse ethnicit
certain way
m “Si Raja B
regarded equ
power, but
aga, 1997:42
a”) represen
a patrilineal,
an groupings
man after the
ractice of th
of the male
and female a
Figure 2
icting Batakne
e can see fro
retically disc
knese. The p
Bataknese an
ussions relat
he discussion
things can b
ties in the co
y to calculate
atak” – liter
uivalent with
merely a na
). Figure 2 s
ts who the r
, thus the na
s. There are
e previous o
is patriarchy
e’s family lin
among Batak
ese Clan Tree
om the socia
cussed with
paper raises
nd some ce
ted to the p
ns how Bata
be learnt fro
e from the r
rally means
h other Indo
ame of hono
hows the gr
respective an
ames of the
however, s
one passed a
y, Bataknese
es – a practi
al phenomen
broader th
some discus
rtain traditio
population o
knese can be
om this clan
respective ge
the “king of
onesian ethn
or attached t
oupings of t
ncestor is. It
mothers are
ome ancesto
away – yet
female who
ice that also
na of this
ssions on
ons kept
f growth
e related
n‐tree of
f batak”.
nic group
o him by
he Batak
is worth
e not yet
ors were
sons are
o marries
who has
and Raja
from the
Batak p
is the ol
least in t
note the
and rela
the soci
and intr
the com
is about
get mar
his moth
Figure 2 sho
s two noted
a Isumbaon.
e same gene
eople that
hers from 6th
nealogical tre
dest clan gro
the earlier g
e web of the
It is interest
ationship am
ial identities
e among Ba
ra‐ethnic soc
mpletely socia
t the family
gs. For insta
ried and the
her as wife (‘
ows us the li
children tha
The names
erations – fu
become the
h upto 9th ge
ee as a matt
oup in the sa
enerations f
clans upto 8
mation of the
ting to see th
mong Batakne
s and affiniti
taknese, fam
cial relations
al life regard
y line, marri
nce, the mal
ere is a kind o
ineages of B
at became th
of clan take
urthermore t
e names of
enerations fr
ter of fact, re
ame siblings,
from the Si R
8th generatio
Bataknese Fa
hat the exist
ese people w
ies that wou
mily living, a
hip. The imp
ding to the cu
iage become
le from the s
of tendency
Batak clan gr
he source of
en from the
there are sto
clan. The n
rom the Si R
egarding to s
, etc. Noneth
Raja Batak. W
n (‘sundut’).
Figure 3
mily‐Tree into
ence of surn
wherever th
uld be very
nd a lot mo
portance of
ustomary law
es an impor
same with fe
for male to
oups from t
f the clans o
name of the
ories, legend
ames of cla
Raja Batak.
some custom
heless, in som
We use the ta
o Graph‐Theo
name plays a
ey are until
important w
ore things re
clan groups
w of Batak. F
rtant things
emale from t
get take fem
he first Bata
r “marga”, i
e old times B
ds, or folklore
ans labeled
There are so
mary law rela
me cases the
arombo as d
retical Topolo
major role
now. The m
when we tal
elated to the
among Bata
the way B
the same cla
male from the
aknese in the
.e.: Guru Ta
Batak people
es on each n
from the Ba
ome version
ated things,
ere are simil
drawn in figu
ogical Web
in social inte
marga or clan
lk about ma
e traditional
ak people pe
e, since the d
atak keeps
an (or groups
e same clan
e center,
e are not
names of
ns of this
like who
arities at
ure 2 that
n reflects
ating and
the clan
s) cannot
group of
they wo
with in‐l
by using
3. Some
We tran
Batak Cl
A very fund
ary rule for
e among Bat
“The Somba
“Elek Marbo
“Manat Mar
en (1964) di
d as the fam
ese meets an
ould have fou
laws), “dong
s of Batak ha
g the networ
e Insights fro
From our u
related to th
nsform the c
r interesting
lan from the
Campos & d
ion emergin
can only o
damental cu
social living
taknese. The
a Hula‐hula”
oru” (be kind
rdongan Tub
scusses this
mily name a
other Batak,
und the conn
gan tubu” or
as given an i
k model sho
om Bataknes
he growth of
chart in figu
facts about
The expone
first genera
de Oliviera
ng the scale
occurred wh
ustomary la
g and statu
e Dalihan Na
” (pay respe
d to the famil
bu” (keep the
in detail. Ye
among Batak
, they will int
nections betw
“dongan sab
interesting q
wn in the ne
se Clan‐Tree
ng on Batak
f the earliest
re 2 into the
the relatedn
ential rate of p
tion to the e
(2003) discu
‐free behav
hen there i
aw in Batak
s related to
Tolu is the t
ct to the fa
ly of son‐in‐l
e warm brot
et, what we
knese is ess
troduce them
ween them,
butuha” (the
questions, ho
ext section o
knese clan, w
t Batak peop
e one showe
ness of a clan
Figure 4
population gro
ussed an ev
ior that foll
is no const
nese people
o the affinit
hree basic la
mily of the
aw and the r
herhood fro
want to sho
ential to Ind
mselves by u
be it as “hul
e same clan o
ow a clan gr
f the paper.
we would l
ple from Si R
ed in figure
n to another
owth in Batak
volutionary m
lows the Ma
traint of ca
e is called
aws among B
wife’s paren
related clan)
m the same
ow here is th
donesian Ba
using their su
la‐hula” or “
or group of o
oup really co
ike to discu
Raja Batak to
3. From thi
by using the
k Family Tree
model relate
althusian gr
arrying capa
Dalihan Na
hip of, to, a
Batak people
nts and the
), and
and related
hat the nam
tak people.
urnames. Aft
boru” (the sa
one). This int
onnected to
uss some int
o the 8th gen
s transforma
e tarombo.
ed to the gr
rowth. A Ma
acity of the
a Tolu, a
and from
e, i.e.:
e related
e of clan
When a
ame clan
o another
ation we
rowth of
e natural
environment. We plot the growth of the numbers of noted names in the tarombo and interestingly
find a sort of Malthusian growth rate (of man, since the family tree does not contain the names of
the woman at the respective generation) of
mn =m0 exp(ρn) (1)
where n m denotes the name in the n‐th generation (“sundut”) and ρ denotes the growth rate. This
is showed in figure 4. The exponential rate happens to be in Malthusian simple model is
understandable for at the estimated year of earlier Bataknese is in 1200s (Sinaga, 1997) where
natural capacity was not a really matter for population growth in northern Sumatera.
Closeness Among Bataknese Clan
The Tarombo can be seen as directed graph of G(V,E), where the names of the individuals
(most of them become the names of Bataknese clans) are represented by the vertices (V) of the tree
that can be regarded as a family‐web and the edges (E). In our visualization, however, we can
present the graph in the directed network which arrows showing the directions of fathers to sons for
the nature of patrilinial Batak’s customs. In order to extract some interesting properties from the
clan‐genealogical tree, we employ the random graph concept by looking at the network as the set of
N vertices that are connected each other with independent probability p. A similar problem has
been pointed out by the seminal work on random graph related to the problem in mathematical
genetics of Solomonoff & Rapoport (1951). Thus, the graph n,p G that according to Erdös & Rényi
(1960) should exhibit the binomial degree distribution. The probability x p that a randomly chosen
node is connected to exactly x others can be written,
x (1 )n x
p p p
− ⎛ ⎞
=⎜ ⎟ −
⎝ ⎠
lim (1 )
! 1
x x
x n
p n p p
→∞x p
⎛ ⎞
= ⎜⎝ − ⎟⎠ −
exp( )
z z

􀀑 (4)
that is the so‐called Poisson distribution. However, what we found in the clan‐tree is not actually the
Poisson distributed interconnectedness. As it is shown in figure 5, the degree distribution in
Bataknese clan‐tree happens to be the fatter‐tail of the power law,
x p xα ∼ (5)
with exponent 3.0209 (R=0.93787)1. The nature of this exponent is somehow different on some
other networked systems we have seen before (e.g.: Situngkir, 2007) for the it’s value is > 3. Reading
the proof shown by Cohen & Havlin (2003), we can say that the diameter is not really ultrasmall2.
1 We use the standard Kolmogorov‐Smirnov statistical test (Clauset, et. al., 2007) and calculate the maximumlikelihood
of the exponent of the power‐law.
The top
been de
G0(r) =
where p
x p
The diam
d 1
= Σ
2 Ultrasm
ology of the
epicted in Ne
ing function
cted from th
p r

x is the pro
tion suppose
lity x p is giv
0 !
d G
dr =
meter of the
( , )
δ i j
= Σ
mall diameter
The d
clan‐tree ca
ewman, et. a
ns. The clan
e generating
obability func
edly can be n
ven by the xe
Batak clanhappens
in th
degree distrib
an thus be re
al. (2001), w
network th
g function
ction that a r
th derivative
‐tree (the av
he small‐world
Figure 5
ution of Batak
egarded not
we can do th
at is compo
randomly ch
thus 0 G (1) =
e of 0 G ,
erage minim
d topology of
knese clan ne
t‐really a sma
e simulation
osed by larg
osen node in
1. As show
mum path len
which 2 <α
all‐world top
n to see this
ge amount o
n the graph h
wn in Newm
ngth among
< 3 (Cohen &
pology. As it
in the natu
of N vertices
has degree x
an et. al. (20
nodes) as ca
Havlin, 2003
has also
re of the
s can be
. As the
001), the
where δ (i, j) =min(dij) and ij d is the minimum path‐length between two nodes in the clan‐tree, is
d = 9.4438. The diameter of the generated web is smaller, approximately 3 generated d ≈ .
Interestingly, we can see that the exhibited scale‐free does not represent a really close clans one
another. This closeness could also be seen in the clustering coefficient that can be calculated as
1 N
N =
= Σ (9)
1 ;
i ij jk
i j k jk
C e e
= ∈Γ <
⎛ ⎡ ⎤⎞
= Γ ⎜⎜⎝ ⎢⎣ ⎥⎦⎟⎟⎠
Σ Σ (10)
( ,2) ( 1)
i i
i i
C k k k

Γ = = (11)
Our calculation shows that the general coefficient clustering is 0.0016 not very clustered network
with the one we have from the simulation with the same graph generated before, C ≈ 0.012 .
The power law distribution in the Bataknese clan‐web shows the property of the topological
properties of how the major “hubs” of the clan are closely followed by smaller ones and these
smaller ones are also followed again with even the smaller ones showing the robust topology. As
discussed in Barabasi (2003) this kind of topology has interesting properties of fault tolerant
behavior. As it has been discussed in the beginning of the paper, there are sometimes debates
among descendants about the positions of certain clan in the lines of the tarombo, the likelihood
that a hub would be affected the macro properties of the system is unlikely. The acknowledgement
of Bataknese to the clan hubs are somehow becoming the key factor that made the network robust
from time to time.
4. Concluding Remarks
We have discussed short anthropological features of Batak family tree or clan‐genealogical
tree and how it affects and is influenced by the traditional customary laws in social life, even until
today’s modern life. The occurrence of Malthusian growth model is also found in the earliest Batak
community for there is no significant environmental capacity problem at the time. Furthermore, we
have shown the diameter of the Tarombo Batak (family tree) showing how closely related a clan to
another. We found the scale‐free behavior in the clan‐web and see that even though there are some
debates on the construction of family tree right now among Bataknese, the robustness of the chart
of the family tree is still persist for the general acknowledgement of the hubs – a property emerges
from the topology of the scale‐free network.
A lot of works can be directed from this work in modern anthropological approaches to
genealogical tree. For instance, most of Bataknese kept their family tree altogether rooted from the
top to the bottom and analyzing the statistical properties of this can be useful to understand a lot of
things related to this. Another work can also be conducted by computational simulations on how the
fundamental of Batak traditional customary law would emerges such statistical properties. A more
comprehensive approach to enrich our understanding on anthropological works of complex
Indonesian Batak people is open.
Works Cited
Barabási, A‐L. (2003). Linked: How Everything is Connected to Everything Else and What It Means for
Bussiness, Science, and Everyday Life. Plume.
Bouquet, M. (1996). “Family Trees and Their Affinities: The Visual Imperative of the Genealogical
Diagram”. The Journal of the Royal Anthropological Institute 2(1): 43‐66.
Campos, P. R. A., de Olivieira, V. M. (2003). “Scale‐free Networks in Evolution”. Physica A 325: 570‐6.
Cohen, R. & Havlin, S. (2003). “Scale‐Free Networks are Ultrasmall” Physical Review Letter 90,
Clauset, A., Shalizi, C.R., & Newman, M.E.J. (2007). “Power‐law distributions in empirical data”. Preprint
Erdös, P. & Rényi, A. (1960). “On the Evolution of Random Graphs”. Publications of the Mathematical
Institute of the Hungarian Academy of Sciences 5: 17‐61.
Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2001). “Random Graphs with Arbitrary Degree
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Serva, M. (2004). “Lack of Self‐Averaging and Family Trees”. Physica A 332: 387‐93.
Sinaga, R. (1997). Leluhur Marga‐marga Batak dalam Sejarah, Silsilah, dan Legenda. Dian Utama.
Situngkir, H. (2003). “Cultural Studies through Complexity Sciences: Beyond Postmodern Culture
without Postmodern Theorists”. BFI Working Paper Series WPM2003.
Situngkir, H. (2004). “On Selfish Memes: Culture as Complex Adaptive System”. BFI Working Paper
Series WPG2004.
Situngkir, H. (2007). “Conjecture to Statistical Proximity with Tree of Language (?)”. BFI Working
Paper Series WPI2007.
Solomonoff, R. & Rapoport, A. (1951). “Connectivity of Random Nets”. Bulletin of Mathematical
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Vergowen, J. C. (1964). The Social Organization and Customary Law of the Toba‐Batak of Northern
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