Traditionally, social networks are regarded as interaction patterns between people. Since organizations also interact and are composed of people then the notion of social networks may be extended to these entities. Furthermore, in some industries, interactions between organizations take place in a somewhat well defined environment in which quantitative data may be readily extracted. This research explores how that data may be used create a mathematical model that depicts the interaction patterns between organizations. The interaction data used are transactions in the Indonesian inter-bank money market. Individual behavior is modeled as a multiple linear regression equation with the weighted average of the bank’s lending rate in the market and the environmental variables regarded to have some effect in determination of the bank’s rate (in which some are controllable by the central bank) as the dependent and independent variables, respectively. Afterwards, the resulting model can be incorporated in the policymaking process of the central bank.

1. Social Cluster Analysis of Interbank Money Market Transaction Behavior
using Markov Clustering Algorithm
Sasmito Adibowo, Marisa Prawiraatmadja
School of Business and Management, Bandung Institute of Technology
Abstract – Traditionally, social networks are regarded convictions; parallel of which is the concept of company
as interaction patterns between people. Since organizations values. Based on this analogy, the model of social clus-
also interact and are composed of people then the notion of ters in human interaction may be extended to include the
social networks may be extended to these entities. Further- ‘social’ clusters in dealings between corporations.
more, in some industries, interactions between organizations An advantage of analyzing interaction data of organi-
take place in a somewhat well defined environment in which zations from those of people is that the former tends to be
quantitative data may be readily extracted. This research more structured and thus quantitative data may be more
explores how that data may be used create a mathematical readily extracted. Generally, transactions between corpo-
model that depicts the interaction patterns between organi- rations are officially recorded and even some types may
zations. The interaction data used are transactions in the have to pass through a governing body – which in turn
Indonesian inter-bank money market. Individual behavior maintains data for archival purposes. One example is in
is modeled as a multiple linear regression equation with the the Indonesian interbank money market in which com-
weighted average of the bank’s lending rate in the market mercial banks engaged in short-term loan transactions
and the environmental variables regarded to have some ef- must do so via the central bank.
fect in determination of the bank’s rate (in which some are The Central Bank of Indonesia (BI: Bank Indonesia)
controllable by the central bank) as the dependent and inde- has an interest in mining data of interbank transactions as
pendent variables, respectively. Afterwards, the resulting a way to obtain feedback for policymaking. A goal of the
model can be incorporated in the policymaking process of organization is to control the nation’s inflation rate. Fur-
the central bank. thermore, its research has established that interest rates
formed in the inter-bank money market is a leading indi-
Keywords – data mining, behavioral finance, Markov cator of inflation [3]. Thus mining the market’s transac-
Clustering, multiple linear regression, social network, soft tional data on how the interest rates are formed should
computing. provide useful information on how the government body
could utilize its instruments to affect the market.
I. INTRODUCTION This research attempts to elicit the emergent social
clusters among banks in the Indonesian interbank money
Interaction patterns between people rarely take the
market and analyze their group behavior. It is among
form of an evenly-spaced grid; more often there are
those that apply a soft-science theory using a hard-science
groups of people who interact more extensively than oth-
approach for purposes of data mining. The behavioral
ers. This clustering may due to geographical proximity,
theory of social clusters is applied using a computational
personal compatibility, or even professional demands, to
method and analyzed via multiple linear regression statis-
name a few. According to organizational behavior theory
tics. Although the research’s domain is in the financial
[4], these social clusters are categorized into emergent
industry, it is in the authors’ hope that the method may be
clusters and prescribed clusters. Emergent clusters are
extended further to other domains that involves data min-
those formed from the grassroots level whereas pre-
ing.
scribed clusters are imposed upon by an authoritative
body. The peer group is an example of emergent cluster II. METHODOLOGY
whereas a department is one example of a prescribed
cluster. When people are aggregated in a structured man- Input data were extracted from the transactions in the
ner in an organization, the latter may exhibit person-like interbank money market for the period between January
traits. A human being has a personality; likewise there is 2, 2001 and July 20, 2003 inclusively. They were pro-
a notion of corporate culture. People have moralities and vided in the form of a table by the central bank’s staff and
The 2nd Indonesia Japan Joint Scientific Symposium 2006

2. Page 2 of 5
encoded to conceal the transacting bank’s identity (in sbi_1 Poly. (sbi_1)
accordance to the banking regulations of non-disclosure). 20 %
Each row in the table contains: 18 %
16 %
the date and time of the transaction – in which 14 % Period 2 No Transaction
(transition) Data
Interest Rate (Percent)
the fund transfer took place; 12 % Period 1
(contraction) Period 3
(expansion)
the lending bank’s encoded name;
10 %
8%
the receiving bank’s encoded name; 6%
Period 4
(expansion)
the loan amount. 4%
the interest rate of the loan.
2%
0%
Social interaction is then modeled as a directed graph
2001-01-02
2001-03-02
2001-05-02
2001-07-02
2001-09-02
2001-11-02
2002-01-02
2002-03-02
2002-05-02
2002-07-02
2002-09-02
2002-11-02
2003-01-02
2003-03-02
2003-05-02
2003-07-02
2003-09-02
2003-11-02
2004-01-02
2004-03-02
2004-05-02
2004-07-02
in which the edges are based on the transactions that took Effective Date
place. It is postulated that banks who often lends large
Fig. 1. SBI-1 rates and period subdivisions.
amounts of money to some other banks with low interest
rates are considered as socially closer (as in friends) with as a loan) therefore its rate is actually a weighted average
those banks. In order to measure this level of friendship, of the interest rates set by the auction winners.
values – that the authors refer as the proximity index – are For each period the corresponding interaction graph
attached as the weights of the graph’s edges in which the was constructed. There were about 100 banks involved
greater the index value means that the lending bank is so that the process was too tedious to be performed by
more acquainted with its counterpart and thus have a hand and thus a computer program was developed to con-
higher trust level. Note that – as in person-to-person in- struct the graphs and calculate the edge weights. An at-
teraction – trust level is not bi-directional; if A trusts B tempt was made to use Graphviz1 (a program to layout
with a level of 3.5 it may be the case that B’s trust level to graphs in such a way to optimize it for humans to visual-
A is only 1.8 since B is more cautious than A. ize) to render the graphs but due to the large number of
n vj nodes and edges, the resulting images were too complex
P( x, y ) = ∑ ( ) (1) to be comprehended visually.
j =1 ij The resulting interaction graphs were then input into
Equation (1) defines the proximity index. P(x, y) is the the TribeMCL program [2] for Markov Cluster process-
weight of the directed edge from bank x to bank y, in ing. This algorithm was chosen because the use of liquid
which the reverse direction will have its own weight de- flow simulation is a good representation for the flow of
noted by P(y, x). The subscript j denotes the transaction money between the banks, which in turn is a surrogate for
number in which bank X lent to bank Y; each transaction the flow of trust that the authors were seeking to infer.
has a loan amount denoted by vj and an interest rate de- In short, the algorithm simulates the flow of fluid in a
noted by ij. directed graph using edges as pipes in which it may flow
The time span of the analysis is further subdivided between the nodes. Initially a random set of nodes are
according to periods of expansion or contraction policy selected in which fluid starts flowing to other nodes as per
regime in the central bank. In expansion regime, the cen- the direction of the edges and flows faster in edges with
tral bank generally aims to increase the flow of money in larger weights. Afterwards the process continues itera-
the community, which is reflected in decreasing bond tively by increasing the flow in those edges in which the
rates whereas in contraction regime the opposite occurs. fluid is fast and reducing the flow in those that has less
The interest rate used to mark the partitions was the rate current. Then edges that have slow currents are gradually
of SBI-1 (SBI: Sertifikat Bank Indonesia), the one-month removed from the graph until a stable condition is
BI bond certificates. As Fig. 1 shows, there was one con- reached. The result is a set of clusters (or puddles, in
traction period, a transition period, and then followed by terms of liquid) in which liquid tend to flow among the
two expansion periods. The point of divisions between member nodes. Fig. 2 illustrates the process in which the
periods was rather arbitrarily chosen based on sharp upper-left image is the initial graph and the lower-left
changes that occur in the chart. In the second expansion image shows the resulting clusters.
period, decline of SBI-1 rate is leaner than the first. Note For each bank in each period of transaction, a linear
that SBI bonds are auctioned in a quantity-based manner regression model (2) was constructed in which the de-
(based on the total amount of money to be made available
1
Graph Visualization Software – available: http://www.graphviz.org/

3. Page 3 of 5
PUAB j – the interbank money market weighted
average interest rate (PUAB: Pasar Uang Antar
Bank) in day j.
Rj-1 – the bank’s weighted average loan rate in
the previous day (day j-1).
Result of the regression model (2), the constants a0..a7
were normalized to obtain β-values that measures the
relative importance of the corresponding independent
variables. Additionally t-statistic tests (using α=5%)
were performed on the equations to determine which β-
values are statistically significant. Those β-values that
did not pass the t-test are nullified since the fact signifies
that the related independent variables are regarded as rela-
tively unconsidered by the bank. Whereas the β-values
that passes the test are ranked from the greatest to the
least magnitude to infer the order of priority of the bank’s
decision-making process in determining its interest rate.
Fig. 2. Graph Clustering by Flow Simulation process [2]. Having obtained individual behavior, processing is
then continued in the cluster level. For each clusters, the
pendent variable is the bank’s weighted average of outgo- frequency of priorities of each independent variables are
ing loan interests. The independent variables consists of calculated. As shown in (3), fr,i is the number of banks in
interest rates of various deposit instruments provided by a particular cluster that places the i-th independent vari-
the central bank, two market variables, and the bank’s able as priority r in determining its loan rate, taking ac-
own weighted average loan interest rate in the previous count only β-values that passed the t-test (denoted as β').
day. The basic idea of the equation is to infer the bank’s Weighted average values Wi are then calculated over
decision-making process of determining its loan rate by these frequencies, which in turn are ranked from the
measuring the relative importance of these variables in greatest to the least valued to obtain the relative impor-
the process. tance of the i-th independent variable for the cluster.
R j = a0 + a1 × SBI_1j + a2 × SBI_3 j 7
1
Wi = ∑ ( × f r,i )
+ a3 × FASBI j + a4 × SOR j + a5 × USD j (2) r =1 r
n ⎧ ; rank( β ' ) = r
(3)
+ a6 × PUAB j + a7 × R j −1 ⎪1
f r,i = ∑ ⎨
ι
Rj – the average loan rate provided by the bank in ⎪0 ; rank( β ι' ) ≠ r
⎩
the money market for day j.
SBI_1j – the interest rate of the one-month SBI III. RESULTS
bond certificate for day j.
SBI_3 j – the interest rate of the three-month SBI In the first period of contraction which spans from
bond certificate for day j. 1-Jan-2001 to 24-Aug-2001 there were only three clusters
FASBI j – the interest rate of the BI savings ac- in which one is regarded as dominant since it comprises
count (FASBI: Fasilitas Simpanan Bank Indone- of 91 members out of the 101 banks which performed
sia) for day j. transactions during the period, as listed in Table I. Af-
SOR j – the stop-out rate2 of SBI_1 auction for terwards in the transition period that ends in
the day j. 26-Apr-2002, the number of clusters rose to seven in
USD j – the median exchange rate of the Rupiah which two are dominant comprising of 47 and 18 out of
against US Dollar in day j. 96 banks in the period. Following that, the first expan-
sion period ending at 4-Oct-2002 in which there was a
2
Noting that SBI is offered in a quantity-based auction, the stop-out rate rather sharp decrease in the SBI_1 rate, the market seems
is the highest winning discount rate of a bid session. to be further broken up to twelve clusters, similarly with
two dominant clusters of 33 and 17 members out of a
total of 97 banks. In the final period of expansion which

4. Page 4 of 5
ends in 20-Jul-2003 – which is also the end of the time PERIOD 1 PERIOD 2 PERIOD 3 PERIOD 4
span of observation – the market seemed to be consolidat-
Cluster B2
ing since the number of clusters was reduced to nine with 47
Cluster A3
33
one dominant cluster enclosing 82 of a total of 117 banks.
Table I lists the ranks of weighted average of priority Cluster A1
Cluster C4
frequencies Wi defined in (3) for each cluster in each pe- 91 82
riod for the independent variables; with the PREV column
being Rj-1 in (2). Clusters are named with a letter and a
number designating the period; cluster B1 is the second Legend
Path P
Cluster C2 Cluster C3
cluster (in arbitrary order) in the first period. The domi- Path Q
Path R 18 17
nant clusters and their priorities are printed in boldface. Path S
Hyphens in the priority cells denote that none of the clus-
Fig. 3. Movement of banks between dominant clusters.
ter members are sensitive to the corresponding independ-
ent variables – in other words, none of the members’ β- based on their movements among these clusters in the
values pass the t-test for the independent variable. time dimension.
Additionally an attempt to analyze the behaviors of Fig. 3 illustrates the possible paths that may be trav-
the market makers and the roles they play in the clusters ersed by the banks along the major clusters (see Table I
was performed. However since the identities of the banks for the definition of the clusters). Path P starts from clus-
were inaccessible, likewise the identities of these market ter A1 (Cluster A in Period 1), goes to B2, and so forth.
makers as according to the central bank. Therefore, the Path Q stopped at C3 – there were no banks which trav-
next best alternative was to identify them by proxy of eled that path and finally became a member of C4.
those banks who consistently being members of major Path P travels through the larger of the dominant
clusters in all four periods. Primarily the analysis was clusters and consists of eight banks. Banks in this cluster
almost exclusively rely on the market rate and a few from
TABLE I its own previous day rate in determining its interest rate
CLUSTERS AND RELATIVE PRIORITIES IN EACH PERIOD offered to the market. Since these banks tend to ignore
Period Clus- Num Priority the other independent variables, it is suspected that these
ter Banks SBI_1 SBI_3 FASBI SOR USD PUAB PREV banks are the dominant players that control 80% of the
1 A1 6 - - 2 - - 1 3
(contrac- B1 91 - - 3 5 4 1 2 market according to a previous research conducted by the
tion) C1 4 - - - - - 1 2 central bank [1].
A2 7 - - - - 3 1 2
B2 47 3 4 - 6 5 1 2
Path Q travels through the lesser of the dominant
2
C2 18 - - - - 3 1 2 clusters and consists of sixteen banks. The behaviors of
D2 6 - 2 - - 2 1 4
(transition)
E2 6 - 3 - - - 1 2
these banks are generally identical to those in Path P al-
F2 3 - - - - 3 1 2 though some also seems to observe the US Dollar ex-
G2 9 - - - - 3 1 2
change rate. It is probable that they attempted to form
A3 33 3 - 4 4 6 1 2
B3 2 - - 2 - - 1 - their own coalition but segregated out when the market
C3 17 2 6 7 4 5 1 3 re-consolidates in Period 4.
D3 3 2 - 1 - 5 4 3
E3 3 - 5 2 - 4 1 2 There were thirteen banks in Path R in which they
3 F3 5 1 - - 3 - 2 4 first joined the larger dominant cluster in Period 2 but
(expansion) G3 3 - - - - - - -
H3 8 - - - - - - - then moved to the lesser one in Period 3. Behaviors of
I3 6 - - 3 - 4 1 2 the banks in this path are considerably more varying than
J3 5 - - 2 - - 1 -
K3 10 - - 3 - - 1 2 those in Path P. Although generally the market rate and
L3 2 - - - - - 1 - its own rate still takes priority, more banks in this path
A4 3 4 - - 1 - 3 1
B4 4 - - 2 - - 1 2
also takes account the other variables into consideration.
C4 82 3 6 4 2 7 1 5 Finally, the twelve banks in Path S first traveled to
D4 8 2 4 3 - - 1 5
4
E4 3 2 6 4 1 7 5 3
the lesser dominant cluster in Period 2 to join the larger
(expansion)
F4 8 - - 2 - 3 1 3 dominant cluster in Period 3. The behaviors of these
G4 2 3 - - 1 1 5 3
H4 3 - - 2 - - 1 3
banks are generally similar to those in Path R.
I4 4 - - - - 3 1 2

5. Page 5 of 5
IV. DISCUSSION pothesis that organizations as an entity do exhibit people-
like behaviors. However, it still needs to be shown how
From Table I it is apparent that members of dominant far this analogy can be extended. One counterargument is
clusters tend to be more sensitive to the given environ- that conflicting interests among people does exist in an
mental variables (the independent variables in (3)) in de- organization; this condition normally do not occur inside
termining their interest rates whereas members of non- an individual, except for perhaps cases of psychological
dominant clusters seemed to use other parameters in set- disorders.
ting their interest rates in the interbank money market. As a closing remark, modeling transactional data as a
This may signify that dominant clusters tend to be more social interaction and basing analysis on the emergent
rational than the others. Nevertheless, there are excep- clusters may provide a better result than treating the entire
tions such as cluster E4 which members also took account market as a monolithic entity. Indeed this research had
of all the environmental variables. shown that organizations do expose a behavior normally
Most banks use the market rate and its own rate as the exhibited by people such that the notion of social clusters
top priorities to determine its loan rate. Table I shows is extensible to these entities. Furthermore, although this
that the PUAB column (the weighted average rate of the research is based on the transaction patterns between
market) independent variables almost always show prior- banks, opportunities may exist to apply the fundamental
ity one whereas the PREV column (the bank’s own rate in concepts to other domains, such as in telecommunica-
the previous day) column shows a majority value of two. tions, stock exchange, C2C (consumer-to-consumer)
Therefore, it is likely that the rates are formed by the mar- online commerce, etc. For example, segmenting mobile
ket and that the central bank’s rates tend to play a less phone subscribers based on their telephone call patterns
significant role. may yield a better pricing scheme than the static market
In times of change, banks tend to be more selective in segmentation techniques based on demographics. This
choosing their counterparts in the money market whereas field of research is still relatively unexplored since proc-
in more stable situations they are inclined to trade freely. essing of large graphs and the availability of interaction
This behavior is concluded from the fact that the number data (both between entities and between human beings)
of clusters increased during the transition period and the are only made possible through the recent advances of
first expansion period and the existence of two dominant information technology.
clusters during those times. On the other hand, when the
situation stabilizes in Period 4, the market seems to be REFERENCES
consolidating and in the process of returning to the cluster
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configuration as it was in Period 1. This may be parallel
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to the human behavior of being more selective in choos-
ture” (In Indonesian), Direktorat Riset Ekonomi dan Kebijakan
ing their allies during times of disadvantages and more
Moneter Bank Indonesia, Jakarta, 31 October 2002.
trusting when their own security levels are high.
[2] Dongen, Stijn van, “Graph Clustering by Flow Simulation,”
V. CONCLUSION Centre for Mathematics and Computer Science (CWI), Am-
sterdam, 2000, Available: http://micans.org/mcl/lit/svdthe-
The Markov Clustering algorithm [2] only groups the sis.pdf.gz
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Since the clustering process essentially attempts to reveal Wahyu Pratomo, “Operational Framework for Monetary Pol-
the peer groups among those banks, it still needs to be icy: A Proposal” (in Indonesian), Direktorat Riset Ekonomi
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nately, non-disclosure of the bank’s identities prevented
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Since the observation shows that changes in the clus-
tering structure has some resemblance how people re-
assess their selection of peer groups, it affirms the hy-