Evol. Inst. Econ. Rev. 4(2): 267–300 (2008)

DISCUSSION

Network Analyses of the Circulation Flow ofCommunity Currency
Nozomi KICHIJI* and Makoto NISHIBE***Department of Economics, Asahikawa University, 3–23 Nagayama, Asahikawa, Hokkaido
079–8501, Japan. E-mail: kichijin@asahikawa-u.ac.jp**Graduate School of Economics, Hokkaido University, Kita 9, Nishi 7, Kita-ku, Sapporo,
Hokkaido 060–0809, Japan. E-mail: nishibe@econ.hokudai.ac.jp
Abstract
The Japanese economy is emerging from a long-term recession following the bubble and isin the economic recovery phase. However, problems stemming from the widening economic
disparity and the decline of local economy have risen. The local economy received a heavy
blow from the reduction in public investment because of public sector reform combinedwith depopulation and aging. Under these circumstances, community currency attracts muchattention as a tool that can simultaneously solve the twin problems of the decline of the local
economy and the decay of the community. However, little research and few studies havebeen conducted to quantify the extent to which community currency revitalizes the local
economy. We participated in the Tomamae-cho community currency experiment andinvestigated its circulation flow. This paper highlights the circulation flow of community
currency using several network analyses. The following results are presented: (1) various
distributions of the networks obey a power-law distribution; (2) the networks display thecharacteristics of a “Small World” similar to those of organisms, (3) directional andweighted network analyses are important; and (4) the double triangle system is effective due
to its complementarity effect because commercial transactions facilitate circulation flow ofcommunity currency for non-commercial transactions, and non-commercial transactions
expand commercial transactions in the local economy.
Keywords: Power Law, Zipf’s Law, community currencies, social experiment, network
analysis, Hokkaido economy.

1.

Introduction

The current economic problems in Hokkaido can be summarized in three points:
predominance of the service sector, a big deficit of interregional trading, and rapid
depopulation.
The proportion of the secondary sector in the Hokkaido Prefecture is below thenational average, and that of the service sector is far greater than the national average.
JEL: Z13, R11, L14.

N. KICHIJI and M. NISHIBE

Since the proportion of the construction industry within the secondary sector is greaterthan the national average, the recent reduction in public investment has had a significant
impact on the economy of Hokkaido. Due to the enormous central and local government
deficits, the promotion of decentralization and the administrative and financial reforms
are on the move. Consequently, the great deal of tax transfers from the central
government to local governments, which covered the deficits of interregional trading andenabled the heavy public investment in construction sector to stimulate local economies,
can no longer be continued. In addition, the process of depopulation is much faster thanthat in other rural areas of Japan.
Thus the Hokkaido economy is faced with far more severe conditions in comparison
to all the other prefectures. A policy of restructuring local areas must be planned andintroduced to address the problems of depopulation and aging, which are spreading
throughout Hokkaido. In other words, it is necessary to activate the local economy andrevitalize the communities to solve such problems. However, as economic development
supported by the central government cannot be maintained, there exist very few methods
for regenerating a regional economy. Even if it were possible to be supported by thecentral government, local economic development based on a wasteful economy must bereconsidered from the viewpoint of environmental preservation. In addition to theexisting woes of Hokkaido, in the latter half of the 1990s, the region suffered from along economic depression caused by a negative wealth effect resulting from the collapseof the bubble economy. Japanese banks were reluctant to lend money, and forced theirborrowers to withdraw funds because of devastating bad debts. In 1997, both Hokkaido
Takushoku Bank Ltd.(the largest commercial bank in Hokkaido) and Yamaichi Securities
Co. Ltd. (the forth largest security company in Japan) collapsed, and the economic
situation was as desperate as the overall financial crisis.
Under these circumstances, the amount of legal tender circulating in local economies
drastically fell and community currencies (CCs)1) have attracted much attention in
Japan2). Toshiharu Kato (Kato, 1998, 2001) proposed a special kind of community

1)
Community currencies possess the following characteristics for accomplishing the aim ofrevitalizing local economies and communities: (1) circulation in relatively small geographical areas orcommunities of interest, (2) non-governmentally operated and issued, (3) non-convertible or restrictedconvertibility; and (4) zero or negative interest-bearing. It is also called local currencies orcomplementary currencies, with slightly different connotations. For example, local currencies often
mean CCs that circulate in confined local areas such as towns or villages. However, in this paper, we
use only the term “community currency (CC)” to avoid any confusion in terminology.

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Network Analyses of the Circulation Flow of Community Currency

currency called “Eco-money” that was supposed to activate mutual aids and stimulatesocial welfare and volunteer activities among citizens and regenerate local communities.
Kuriyama-cho, Takarazuka City, Himeji City, Toyama City, Yamato City and others
grappled with it after 2000, based on his ideas, and succeeded not only in achieving theoriginal goals to some extent but also in connecting the compartmentalized public
administration sectors horizontally. However, Eco-money seems to have its own
drawbacks.
Eco-money is completely separate from commercial transactions in the market
economy because it is designed for use in social welfare and volunteer activities only.
Moreover, Eco-money tends to accumulate in the hands of participants (in particularyounger generations) who have made significant contributions such as providing a snow
shovel or personal shop to other participants (especially elderly people) because theycannot locate the desired services. As a result, Eco-money does not enjoy smooth
circulation among participants.
The author Makoto Nishibe (Nishibe, 2004) proposed the “double triangle system(DTS)” (See Fig. 1) as a solution to the aforementioned problems concerning Ecomoney. It involved a community currency circulation scheme especially designed toenable smooth flow of currency among participants without any stagnation. Using only
the minor cycle (a small triangle), where CC only mediates non-commercial transactions
such as volunteer activities and mutual aid among the local residents, would eventuallylead to stagnation halfway through the circulation as was seen in case of Eco-money. To
avoid this, it is necessary to introduce the major cycle (a large triangle) as a driving force
where CC mediates commercial transactions of goods and services offered by businesses
and industries, the municipality, civil groups, and NPOs, and by making the major cycle
encompass and drive the minor cycle to forge a complementary relationship between
commercial and non-commercial transactions in an integrated cycle of CC. In DTS,
when the participants obtain CC in compensation for non-commercial transactions, they
can spend it for commercial transactions and the CC can circulate more smoothly andspeedily without unintended hoards. This connection between non-commercial andsubsequent commercial transactions can simultaneously create new purchasing power(effective demand) for the participants to buy goods and services in the local shops or
markets. The creation of effective demand via non-commercial transactions increases the2)

After full liberalization of capital movements in the early 1980s, free capital flows generated newrisks concerning instability. Because of this situation, CCs have spread all over the world, particularly
to Western countries since their second boom in the 1980s, following the first one in the 1930s.

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N. KICHIJI and M. NISHIBE

Fig. 1.

Double triangle system.

volume of commercial transactions and stimulates the local economy. On the other hand,
if shoppers obtain CC through commercial transactions, or if individuals purchase CC bylegal tender and request any volunteer work or mutual aid, the recipients of CC offering
the non-commercial transaction will expect them to accept CC because they can use it
for their shopping. This definitely increases the probability of realization of noncommercial transactions and can lead to a growth in the volume of non-commercial
transactions as well.
Therefore, the merits of DTS stemming from a complementary relationship between
commercial and non-commercial transactions in the scheme are twofold as follows: (1)non-commercial transactions of social welfare and volunteer activities create newpurchasing power for local shops that has not existed before and lead to an increase in
the volume of commercial transactions, thus energizing the local economy and (2)commercial transactions of commodities in the local market create new opportunities forvolunteer workers to spend the CC earned through non-commercial transactions for
shopping at the local mall, which increase the volume of non-commercial transactions
and regenerates the local community.
Consequently, we believe that adopting DTS would enable simultaneous achievement– 270 –

Network Analyses of the Circulation Flow of Community Currencyof both economic activation and community revitalization in rural areas. The Hokkaido
Commerce and Industry Association decided to execute an experimental circulation
based on DTS, and planned to choose the implementation group from local commercial
and industrial associations. The Tomamae-cho Commerce and Industry Association was
selected from several candidates. The experimental circulation of Tomamae-cho
community currency (CC) was conducted over 91 days (or three months), from
November 22, 2004 to February 20, 2005.
The purpose of this paper is to demonstrate the network properties of the Tomamaecho CC system and the DTS and demonstrate whether DTS is effective as a CC system.
If we can confirm theoretically and empirically that DTS functions successfully in a local
economy, we can expect it to be useful for improving the conditions of settlement inorder to restrain the process of depopulation. We investigate the characteristics of the
network using network analyses (Nishibe et al., 2005; Kichiji and Nishibe, 2006). It isnecessary to describe the Tomamae-cho CC system before we investigate its network
properties.
2.

The Tomamae-cho CC System

The name Tomamae-cho CC is composed of two elements: Tomamae-cho (“town” inJapanese) and Chiiki-Tuka (“Community Currency” 3)). Tomamae-cho is a small town in
the northern part of Hokkaido in Japan, with a population of about 4,300. Its mainindustries are fishing, forestry, and commerce. Tomamae-cho has recently been facing
problems such as scarcity of job opportunities and spillover of purchasing power torelatively large neighboring towns (with populations of 8,000 or more), in addition to
long-term depopulation and aging, as is the case for other rural areas of Japan. In 2004,
the Tomamae-cho Commerce and Industry Association, in collaboration with theTomamae-cho municipal government, decided to introduce a CC for the purpose of both
economic renewal and community revitalization. This was done on an experimental
basis. The Tomamae-cho CC system is an integrated system with a reusable gift
certificate (See Figs. 2–3) and a shopping stamp (See Fig. 4). Anyone can purchase anduse Tomamae-cho CC anywhere for social welfare and volunteer activities, but its usage
for commercial transactions is restricted to specific business partners within Tomamaecho. Tomamae-cho CC, represented by “P,” has a linear equivalence to yen currency.

3)This is a gift certificate legally redeemable into yen, so that retailers may use it repeatedly for otherpeople or exchange it for money upon receipt from their customers.

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N. KICHIJI and M. NISHIBE

Circulation operates in three ways: (1) Units are issued by the Commerce and Industry
Association and the municipal government of Tomamae-cho when participants purchaseCC with yen4); (2) participants are paid in CC for the services or goods they supply toothers; (3) once participants accumulate 250 stamps (500 points), they can convert these
to a 500P note at the issuing office. Participants receive stamps equivalent to 2% of theamount paid in either CC or conventional money if the trading partner is a specificFig. 2. Front side of Tomamae-cho CC.

Fig. 3.

Reverse side of Tomamae-cho CC.

Fig. 4.

4)2-point stamps.

500 yen can purchase a 500P note plus 10P-stamps as its 2 percent premium.

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Network Analyses of the Circulation Flow of Community Currency

business partner within the scheme. Moreover, individual members and specific business
partners also receive a 2% dividend in stamps of the amount paid when purchasing CC at
the issuing office. Therefore, individual members can benefit from a 4% premium if theypurchase CC with yen and use it with specific business partners. The CC system isdesigned to function as a strong incentive for the individual use of CC. Shops
participated as specific business partners in the experimental circulation of Tomamaecho CC, and only such partners can exchange CC for money. Under this experiment,
specific business partners have to accept the condition that they purchase stamps inadvance and repay the 2% dividend of the amount received in stamps. In 2000, 67.5% ofTomamae-cho’s purchasing power spilled over to relatively large neighboring towns.
The specific business partners had the advantage of including the purchasing power ofthese towns by accepting and using Tomamae-cho CC. Forty nine specific business
partners and 12 group partners agreed to cooperate in the experimental circulation ofTomamae-cho CC. The recirculation of CC within the town was encouraged by theredemption cost of 5 yen on exchanging a 500P note for money.
3.

Follow-up Method for Tomamae-cho CC

We participated in the CC experiment and investigated its circulation flow in a uniqueway. Before the experimental circulation in 2004, our investigation team requested theissuing agents to devise an entry space on the reverse of each CC note in order forrecipients to record transaction dates, their names and addresses, and the purposes of use,
up to a maximum of five recipients. We also asked the participants to agree to cooperate
in our investigation. After the circulation experiment of Tomamae-cho CC, we collected
all the currency notes that had been returned to the issuing agents in exchange for yen,and then created an adjacency matrix from the acquired data in order to analyze thecirculation flow of the CC notes using several network theories.
4.

Statistical Data on the Experimental Circulation of Tomamae-cho CC

Table 1 shows the main statistical data on the experimental circulation of Tomamae-cho
CC. All Tomamae-cho CCs are scheduled to expire at the end of the experimental
period. From Table 1, the velocity of the CC is 5.078. This is 6 to 7 times higher thanthat of yen because the limitation of the period and the circulation domain of the CC
enhances its velocity.

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N. KICHIJI and M. NISHIBE

Table 1.

Statistical data on Tomamae-cho CC.

Experiment period
Number of CCs issued
Total participants (individual, specific business, group)
Turnover of each CC
Number of CC with turnover 1
turnover 2
turnover 3
turnover 4
turnover 5
Total number of circulations of CC
Total amount
Average amount per participant
Velocity of CC (year)5.

11/22/2004 to 2/20/2005
2,192(4/8/2005)
272 actors
1,764
314
77
37
0
2,771
138,5500P
5,093.75P
5.078

Analyses of the Circulation Flow of Tomamae-cho CC

We review the relationship between the adjacency matrix and the network before
performing several network analyses.
5.1

Adjacency matrix

The most common form of matrix in network analysis is a very simple square matrix
with as many rows and columns as actors (nodes, vertices) in the data set (Scott, 2000;
Kanamitsu, 2003; Yasuda, 2001; Masuda and Konno, 2005). The “elements,” or scoresin the cells of the matrix, record information about the ties (links, edges) between eachpair of actors. In our case, “actors” means participants in the experimental circulation ofTomamae-cho CC, and a tie between person A and person B means that person A dealt
with person B using CC.
The simplest and most common matrix is a binary matrix. That is, if a tie is present, 1(one) is entered in a cell, else 0 (zero). This kind of matrix is called an “adjacency
matrix” (See Fig. 5(a)). An adjacency matrix may be “symmetric” or “asymmetric.”
Dealings between person A and person B using CC can also be either symmetric or
asymmetric. For example, person A buys goods and services from person B and gives
the CC to person B. Person B does not buy anything from person A. In this case, theelement in our adjacency matrix showing the relationship of person A to person B would
be scored “1” while that showing the relationship of person B to person A would bescored “0.” That is, in an asymmetric matrix, Xi,j is not necessarily equal to Xj,i .
In our case, an adjacency matrix is either binary or valued, since the flow of the CC– 274 –

Network Analyses of the Circulation Flow of Community Currency

Fig. 5. (a) Adjacency matrix. (b) Adjacency matrix (valued). (c) Network of CC.

Fig. 6.

Network graph of Tomamae-cho CC.

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N. KICHIJI and M. NISHIBE

can be represented by the volume of transactions (See Fig. 5(b)). Let us look at a simple
example. The directional graph of the Tomamae-cho CC network (TCCN) among
persons A, B, C, D, and E is shown in Fig. 5(c). Moreover, in our case, we can show the
TCCN at the district level (e.g., Kotanbetsu district, Tomamae district and Sankei
district), which will be discussed in detail elsewhere. Figure 6 is the Network Graph ofTomamae-cho CC.
5.2

General characteristics of the TCCN from the aspect of degree

Before we analyze the network properties, we must address the terminology. The
terminology used in some network analyses is confusing. In mathematics, “vertex” and“edge” are used; however, in social network analysis, “actor” and “tie” are used.
Moreover, in physics, “node” (vertex) and “link” (edge) are used. We use “actor” and“tie” in the context of social network analysis, and “node” and “link” in the context of
network analysis in physics. We indicated the number of nodes, the average of degree ,the clustering coefficient C5) and the average path length l 6). For comparison, we
included the clustering coefficient Crand and the average path length lrand of a randomgraph of the same size and average degree.
In this section, we analyze the topology of the TCCN. This network is relatively small,being characterized by vertex272 and edge406. The network density is about 0.0055.
The degree of the node ranges between 1 and 53, the in-degree of the node ranges
Table 2.

TCCN
LET-Q
E. coliC. elegans

5)

General characteristics of several real networks.

Size

k

C(Crand)l(lrand)

272
287
282
282

3
12.25
7.35
14

0.204 (0.011)
0.494 (0.043)
0.32 (0.026)
0.28 (0.05)

4.41 (5.1)
2.898 (2.26)
2.9 (3.049)
2.65 (2.25)

The clustering coefficient defines a measure of the level of cohesiveness around any given node. It is

expressed as the fraction of connected neighbors Ci 

2eiki ( ki 1)

where ei is the number of links

between the neighbors of the node i, and ki(ki1) is
the maximum number of possible interconnections among the neighbors of the node. C in Table 2
indicates the average value of the clustering coefficient.
6)
For non-directional, unweighted graphs, the number of edges in a path connecting vertices i and j iscalled the length of the path. A geodesic path (or the shortest path) between vertices i and j is one ofthe paths connecting these vertices with minimum length (many geodesic paths may exist between
two vertices); the length of the geodesic path is the geodesic distance dij between vertices i and j.

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Network Analyses of the Circulation Flow of Community Currency

between 1 and 53, and the out-degree of the node ranges between 1 and 15. The TCCN isasymmetrical about the in- and out-degrees.
The in-degree of the node represents the number of people to whom a participant in
the TCCN sold goods and services. In contrast, the out-degree of the node represents thenumber of people from whom a participant purchased goods or services. The network
balance7) of the TCCN is about 0.11. The overall reciprocity8) is 0.015. These results
indicate that the participants polarized between receivers and payers of Tomamae-cho
CC.
The clustering coefficient is large compared to that of the random graph, whereas theaverage path length is small compared to that of the random graph. This is acharacteristic of “small-world” networks (Watts and Strogatz, 1998). We indicate that the
TCCN is very similar to the network of an organism such as E. coli (Wagner and Fell,
2000) or C. elegans (Watts and Strogatz, 1998), as well as the other CC system of LETSQ9). The result indicates that the networks of socio-economic phenomena are comparablewith the networks of natural phenomena. Since the average degree of the TCCN is small
relative to the other networks, we found that the TCCN is in a growth process.
The information on the TCCN is provided by the degree distribution P(k) defined as
the probability that any given node has degree . It is essential to distinguish between an“exponential” network similar to the usual random graph, for which P(k) decreases
exponentially and rapidly, and scale-free networks, for which P(k) decreases typically as
a power law (Zipf, 1949; Albert and Barabási, 2002; Amaral et al., 2000). In the present
case, the degree probability distribution obeys a power-law distribution. The probability
distribution P(k) displays power-law decay P(k):krk with an exponent g k2.43 (Kichiji
and Nishibe, 2007). In Fig. 7, we adopt the cumulative distribution as the vertical axis.
Therefore, in Fig. 7, the slope is 1.43.
Moreover, we examine the degree of similarity between the neighbors of a node. The
relationships are measured by the average degree of the nearest neighbors of a given
node k7)

Network balance is defined by the correlation coefficient of the in-degree and out-degree of eachparticipant. (Wellman et al., 1988).
8)
The overall reciprocity is the value of Num (Xi,j 0 and Xj,i 0)/Num(Xij 0 or Xji 0).
9)
LETS stands for Local Exchange Trading System. This system embodies the most popular type of
CC; it was initiated in 1983 by Michael Linton in Comox Valley, Vancouver Island, Canada, and is
now used in more than 2,000 districts worldwide. Q is the “monetary” unit of LETS-Q; although it is
not convertible into yen, it is assumed to be equivalent to yen. The CC system was initiated in Japanin November 2001 and is managed by an administrative committee called Q-hive.

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N. KICHIJI and M. NISHIBE

Fig. 7. Log-log plot of the cumulative probability function of the degree distribution of the
TCCN. The straight line is a power-law fit and its slope is 1.43.

Fig. 8. Assortativity of the TCCN showing a slightly disassortative behavior.

∑ kP(k | k ) .

knn ( k ) k

where k is a neighbor of node k. The result obtained for the TCCN is shown in Fig. 8.
Figure 8 shows a slightly disassortative behavior10). We also examine the Pearson
correlation coefficient (r) of the degrees at both the ends of the edges. The value of r is
0.255. All social networks studied have significant assortative mixing. However, thetechnological and biological networks are all disassortative (Newman, 2002). The results
10)
Assortative mixing within degrees means a preference of high-degree vertices to attach to otherhigh-degree vertices. In contrast, disassortative mixing means a preference of high-degree vertices toattach to low-degree vertices (Newman, 2002).

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Network Analyses of the Circulation Flow of Community Currency

Table 3.

In-degree
Out-degree
Receipt
Payment
Velocity

Slope of Figs. 11(a)–12(c) and the monthly velocity.
End of Dec.

End of Jan.

End of Feb.

1.13 (R20.985)
1.60 (R20.991)
0.54 (R20.972)
0.50 (R20.953)
1.17891.19 (R20.983)
2.55(R20.992)
0.76 (R20.963)
1.20 (R20.981)
0.51381.20 (R20.962)
2.52 (R20.985)
0.76 (R20.963)
1.08 (R20.987)
0.8214

Fig. 9. (a) Log-log plot of the cumulative probability function of the link weights. The
straight line is a power-law fit and its slope is 1.02. (b) Log-log plot of the cumulative
probability function of the amount of payment and receipt distribution of the TCCN.

indicated that the TCCN is very similar to biological networks (e.g., a marine food web(r0.247), a neural network (r0.163), etc). In our case, this disassortative mixing
meant that several specific business partners had large degrees, whereas the individual
participants had small degrees.
6.

Directional and Weighted Network Analysis of the TCCN

The value of the weights between pairs of participants ranges between 500P andwmax371,000P with an average value w3,405P. The cumulative probability
distribution P(w) that any edge has a weight w displays a power-law decayP(w):wgw with an exponent gw1.0211) (Fig. 9(a)). The strength of a node is defined as∑ws(i ) 

i, j

j

11)

In the case of the probability distribution, this can be expressed as an exponent of 2.02 (1.021).

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N. KICHIJI and M. NISHIBE

In our case, however, the links are directional (symmetric, asymmetric). We classify
the strength of a node into two categories, as a receiver and as a payer:∑ws(i ) 

i, j

j

∑w

s (i ) i, jjs(i) corresponds to the total receipts of the participant i, and s(i) corresponds to thetotal payments of the participant i. For the TCCN, the strength of a node as a receivervaries between 500P and 383,000P with an average value s12,127P12). As a payer,
this varies between 500P and 415,500P with an average value s5.359P13). The
cumulative probability distribution of the strengths P(s) and the strength P(s) that any
given node has a strength s is fitted by a power law P(s): sg s with exponents

g s0.758 and g s1.08, respectively (Fig. 9(b)). The slope of s is steeper than that ofs. This result shows that the disparity in receipts is larger than that in payments. The
cause of this high level of disparity in receipts is that 31 specific business partners
received more than 90% of the total amount received. In addition, the top 10 specificbusiness partners accounted for 83% of all specific business partners’ receipts. In
contrast, in payments, since the amount paid by the specific partners accounted for only
31% of the total, individual participants had a significant effect on the total amount paid.
6.1

Relationship between degrees and transaction amounts

We show in Figs. 10(a)–(b) the strength of the nodes as a function of their degrees. Thereis a weak correlation between the strength of the nodes and their degrees. The correlation
coefficients are positive. The correlation coefficient of the payments and the out-degrees
is 0.316 and that of the receipts and the in-degrees is 0.485. These results suggest thatweighted network analysis is indispensable for socio-economic network analysis because
the degree relationship is sometimes far removed from the weighted relationship.
7.

Dynamics of the TCCN

We examine the dynamics of the TCCN. Figures 11(a)–(c) shows the in-out degree of the
distributions. These distributions seem to roughly obey a power-law distribution.
However, the exponent of the out-degree distribution was twice as high as that of the in-

12)
13)

The number of receivers is 114 persons.
The number of payers is 258 persons.

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Network Analyses of the Circulation Flow of Community Currency

Fig. 10. (a) Relationship between the strength of the nodes and their degrees. (b) Log-log
plot of the relationship between the strength of the nodes and their degrees.

degree distribution. In these distributions, the higher the exponent, the narrower the
disparity among actors. The disparity of the out-degree distribution was smaller than thatof the in-degree distribution. The reasons for this were that the specific business partners
topped the list of the in-degree distribution as the receiver of the CC, and also that the
disparity among the specific business partners was wide. The out-degree distribution
reflects the trend for the individual participants to top the list of the distribution. If thedisparity among the specific business partners is reduced, the slope of the distribution
becomes more gradual; and if the disparity among individual participants widens, theslope of the out-degree distribution becomes sharper. Figures 12(a)–(c) shows thepayment and receipt distributions of the TCCN. In-degree corresponds to the amountreceived, and out-degree corresponds to the amount paid. The transition of the exponentof the payment and receipt distributions is more clear than that of the in-out degree
distributions.
The ratio of the exponents of in-degree (receipt) and out-degree (payment) may be oneof the important indices for analyzing the flow of CC. Figure 13 shows the relationshipbetween the velocity14) of the CC and the ratio of the exponents. The ratio of the
exponents decreases with the velocity of the CC. This figure suggests that the peak14)

We define the velocity of the CC as the ratio between the transaction amount and the outstanding
issue. On a monthly basis, the velocities at the end of Dec., Jan., and Feb. are 1.1789, 0.5138, and
0.8215, respectively.

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Fig. 11. (a) Log-log plot of the cumulative probability function of the in-out degree
distribution 2004.12. (b) Log-log plot of the cumulative probability function of the in-out
degree distribution 2005.1. (c) Log-log plot of the cumulative probability function of the in-out
degree distribution 2005.2.

velocity of the CC corresponds to 1, which means that the exponent of in-degree(receipt) was equivalent to that of out-degree (payment). In natural phenomena, since theratio mostly tends to be equal to 1 (Albert and Barabási, 2002), the maximum flow may
occur at around 1. In our case, since the ratio is sometimes higher than 1, the flow of theCC may stand still. These results require further study.
In addition, we investigate the relationship between network centralization15) and the15)

Freeman’s mathematical definition for network centralization (Freeman, 1979), the index ofcentralization of a network of actors, is represented by the ratio of the sum of actual difference
between the degree of centrality of the most central actor and that of all the other actors in the networkand the theoretical maximum possible sum of differences in actor degree centrality.

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Network Analyses of the Circulation Flow of Community Currency

Fig. 12. (a) Log-log plot of the cumulative probability function of the amount of payment
and receipt distribution 2004.12. (b) Log-log plot of the cumulative probability function of theamount of payment and receipt distribution 2005.1. (c) Log-log plot of the cumulative
probability function of the amount of payment and receipt distribution 2005.2.

total monthly amount. Table 4 shows the correlation between the network centralizationand the monthly transaction. When the network centralization rises, the flow of the CC
increases, and vice versa. This result may show a characteristic of the flow of Tomamaecho CC. Because of the size of the data, we need further investigation for statisticalrigidity.
8.

Effectiveness of DTS

In this section, we establish the fact that DTS increases both commercial and noncommercial transactions by creating complementary relationships between them in thecourse of circulation paths of CC. DTS can thus promote circulation efficiency of money– 283 –

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Fig. 13.

Table 4.

End of Dec.
End of Jan.
End of Feb.

Ratio of two exponents and the velocity of CC.

Correlation between network centralization and transaction amount.
In-degree

Out-degree

Transaction amount

8.29
4.72
11.07

3.71
1.75
2.21

692000148500531500and provide a solution to the problem observed in the implementation of Eco-money by
preventing CC from stagnating halfway through the circulation. Therefore, we claim thatDTS is an effective money system as CC as well as any currency in general since it canenhance viability and sustainability of currency system by bridging commercial
transactions, which are conventionally classified in economic domain, and noncommercial transactions of volunteer activities and social services, which areconventionally classified in social or communal domains.
We explain the basic idea of DTS to focus on the present issue preliminary to thedetailed discussion on it. It is often said that CC is meaningful because it can induce
people to practice mutual help or reciprocity and create social capital in local
communities. But if participants obtain CC in compensation only for non-commercial
transactions as in the single triangle system (STS) (see Fig. 1), it might not be easy forthem to find any items or services they want. Then CC will stand still in their hands andwill not circulate in the system. When this frequently happens here and there, we must
admit that CC is a good idea but STS is not viable. However, if they can spend it for– 284 –

Network Analyses of the Circulation Flow of Community Currency

commercial transactions as well in DTS, CC can continue to circulate more smoothlyand speedy, changing its holders. As the result of this connection of non-commercial
transactions to commercial transactions, DTS increases subsequent commercial
transactions as well as non-commercial ones. In other words, it will create newpurchasing power (effective demand) for the participants not only to buy goods andservices in the local shoppers or local market but also to ask for volunteer activities andsocial services.
First, we demonstrate that there is a positive mutual complementarity effect between
commercial and non-commercial transactions in DTS under the condition that the
average turnover of currency (circulation frequency of money) is above 1. Let us use anumeric example in a simple model as in Fig. 14. This is a currency circulation tree
diagram, which indicates all divergent circulation paths of a currency in DTS when theturnover is 3. If the face value is 1, the total transaction (X) is 3. Assume that acommercial transaction (c) occurs with probability 0.9 and a non-commercial transaction(nc) occurs with probability 0.1. Then, the expected total volume of commercial
transactions (C) is 2.7 and the expected non-commercial transactions (NC ) is 0.3.
If the currency is only usable for commercial transactions as in the case of legal
tender, all non-commercial transactions must be removed from the tree diagram in Fig.
14. It follows that all subsequent commercial transactions with any non-commercial ones
disappear and a single circulation path with three consecutive commercial transactions(ccc) remains as a possible event. Then, the expected total volume of commercial
transactions without non-commercial ones (C) is considered as 2.439 (0.90.92
0.93). On the other hand, if the currency is only usable for non-commercial transactions

Fig. 14.

The circulation paths tree diagram of the currency.

– 285 –

N. KICHIJI and M. NISHIBE

as in the case of Eco-money, all commercial transactions must be removed from the tree
diagram in Fig. 14. It follows that all subsequent non-commercial transactions with any
commercial ones disappear and a single circulation path with three consecutive noncommercial transactions (ncncnc) remains as a possible event. Then, the expected
total volume of non-commercial transactions without commercial ones (NC) is
considered as 0.111 (0.10.120.13). The sum of such commercial transactions andnon-commercial ones thus obtained is XCNC2.55. This represents the totaltransactions in the case where commercial/non-commercial transactions would be
realized separately with legal tender, and Eco-money.
Commercial transactions with legal tender are supposed to occur with a quite highprobability except during a depression period when people expect deflation and tend to
hoard money. Then, even though the probability of realization of consecutive
commercial transactions decreases exponentially, it still remains relatively high.
However, the probability of non-commercial ones must be low as in this case. Therefore,
the probability of realization of three consecutive non-commercial transactions isextremely low. This is the cause of the problem faced by Eco-money. However, DTS cansolve it by creating new circulation paths in the tree diagram. In the above numericexample, (C/C)1(2.7/2.55)10.107, (NC/NC)1(0.3/0.111)11.702, and(X/X)1(3/2.55)10.1765. These represent the expected growth rate of commercial
transactions, that of non-commercial transactions, and total transactions, respectively,
when we introduce CC usable for both commercial and non-commercial transactions in
DTS. The reason why commercial and non-commercial transactions can grow is thateach kind of transaction functions as a mediator or a bridge to connect the other kind of
preceding and succeeding transactions in a mutually complementary relationship. In
other words, currencies can circulate faster when they crossover and connect two
different transaction domains. Therefore, let us refer to this as DTS’s “growth effect,”“transaction complementarity effect,” or “currency crossover effect.”
Next, we present this proposition in more generic terms. Assuming that theprobabilities of realization of commercial and non-commercial transactions are Pc(0Pc1) and Pnc (0Pnc1)16), respectively, and that the average turnover (circulation
velocity) of a currency note in a certain period r is (0r), we get

If Pc0 and Pnc1, then CC0 and NCNC. If Pc1 and Pnc0, then CC andNCNC0. We ignore these trivial cases in the following discussion.

16)– 286 –

Network Analyses of the Circulation Flow of Community Currency

C
C
NC
NC





r (1Pc )1Pcr

r (1Pnc )1PncrrPc
1  (1Pc )r

The proposition to be proved is formulated as0

The inequality

CC

1 , r 1 ⇒

Pc

C
C

1 

NC
NC

 1 17)

1 is reformulated asCCr (1Pc )1Pcr 1 ⇔ Pcr  rPc  r 1  0Here, we regard the left side of the right inequality as the exponential function of r as
fPc(r)PcrrPcr1(0r, 0Pc1)

We can transform it into a polynomial expression and prove the above inequality.
fPc (r )  Pcr  rPc  r 1
 ( Pc 1)2 ( Pcr2  2 Pcr3  3Pcr4  L (r  3) Pc2  (r  2) Pc  (r 1))r1

 ( Pc 1)2 ∑ iPcri1  0i1

We can also take the first and second derivatives of fPc(r) as
fPc(r)lnPc · PcrPc1
fPc (r )  0 ⇒ r 

 1Pc ln lnPc  lnPc 1

fPc(r)(lnPc )2 · Pcr1and calculate the values of the function and the first derivatives by substituting 0 and 1
into rfPc(0)fPc(1)0

17)

If r0, then

C
C



NC
NC

1 . This is also trivial.

– 287 –

N. KICHIJI and M. NISHIBE

fPc(0) 0,

fPc(1)0

0 Pc 1⇒lnPc 0,

PclnPc1

We further examine the function
r 1⇒fPc(r)lnPc · PcrPc10
lim fPc (r )  Pc  1  0 ,r →∞lim fPc (r )  ∞r →∞r 1⇒fPc(r)PcrrPcrr1 0
0 r 1⇒fPc(r)PcrrPcr1 0
r0⇒fPc(r)PcrrPcr1 0
and create a graph of the function as in Fig. 15.
With regard to non-commercial transactions, we can replace Pc for Pnc in the above
function fPc(r) for commercial transactions and use the same discussion to prove that
NC
NC

1 .

Then, we can conclude that0 Pc 1,r1⇒CC NCNC

0 Pc 1,0 r 1⇒C C NC NC

Fig. 15.

Function of fPc (r).

– 288 –

Network Analyses of the Circulation Flow of Community Currency

Namely, if the average turnover (circulation velocity) of the currency (r) is larger than
1, then the commercial and non-commercial transactions expected to be simultaneously
realized in DTS (C and NC) are larger than those expected to be realized separately withdifferent currencies specifically for each transaction (C and NC). Therefore, the totaltransactions in DTS (XCNC) are also larger than XCNC, i.e., XX.
Tomamae-cho CC permits only specific business partners (local shops, stores, andcompanies) to convert the CC into legal tender (yen); however, we have so far ignored
this factor for simplicity. Now, we introduce convertibility of the currency in the modeland examine whether it affects the above results.
Specific business partners receive the currency notes after all the commercial
transactions are made through the CC, and they have to make the following two-stepdecisions: (1) they decide whether or not to convert the received CC and (2) if thedecision to convert is negative in (1), they decide whether to use it for commercial or
non-commercial transactions18). We assume that the probability of conversion of the CC
into yen done by specific business partners is Py (0Py1). Then, the probability thatspecific business partners use the CC for commercial transaction is Pc (1Py)Pc, and for
non-commercial transactions is Pnc(1Py)Pnc(1Py)(1Pc).
First, we take another numeric example. A new parameter Py is set (Py0.8) and theother parameters are the same as before (r3, Pc0.9, Pnc0.1). Figure 16 is the CC
circulation tree diagram in this case.
The commercial transactions that remain when non-commercial transactions are
removed are C0.90.9 0.180.9 0.18 2 1.09116. The total commercial
transactions in DTS are CC0.090.01620.01620.0091.22256, and then,
C/C1.1204 (see Fig. 17). The non-commercial transactions that remain whencommercial transactions are removed are NC0.111, and the total non-commercial
transactions are NC0.13584 and NC/NC1.2238. In this example, commercial
transactions grow at a rate of 12.04% and non-commercial ones grow at 22.38%.
In generic terms, we can express C and C and show that C C.
CPc (1Pcr )1Pc

( Pc ≡ (1Py ) Pc )CC(1Pc)Pc(2Pc2Pc) C18)

We observed that specific business partners converted the CC they received through noncommercial transactions in a very small volume. In the meantime we ignore it for simplicity.

– 289 –

N. KICHIJI and M. NISHIBE

Fig. 16.

The circulation paths tree diagram of the currency with conversion.

Fig. 17.

Event probabilities for each turnover.

2Pc2Pc1⇒(1Pc)Pc(2Pc2Pc)(1Pc)Pc0

Similarly, we can express NC and NC and show that NC NC.
NC

Pnc (1Pncr )1Pnc

NCNCPcPnc(1Pc2Pnc)NC
In DTS with convertibility, the transaction complementarity effect to increasetransactions still works. It is thus proved that DTS is effective in case of convertible
currency notes. However, when convertibility is possible, the currencies go out ofcirculation rapidly. The percentage of currencies converted into yen at turnover 3 is
– 290 –

Network Analyses of the Circulation Flow of Community Currency

92.16%, which makes the circulation velocity of the currency tend to decrease; however,as long as r1, its money crossover effect is still positive.
Next, we make the Tomamae-cho CC circulation diagram based on the above modelwith convertibility by using the real data obtained from the first circulation experiment.
We can distinguish commercial transactions from non-commercial ones based on thedata acquired from the reverse side of the Tomamae-cho CC notes. We define the
combination of commercial and non-commercial transactions as the total transactions.
Figure 18 is the Tomamae-cho CC circulation tree diagram based on the real data.
Note that the numbers in the square signify the number of currency notes that wereconverted subsequent to the commercial or non-commercial transaction at the reference
turnover, and the numbers attached to arrows19) signify the number of currency notes incirculation through the reference circulation path. We can see that all currency notes are
circulated through only two paths (cccc and ncccc), and if we take noncommercial transactions off the tree, ncccc is no longer available. Later, we willcompare this diagram of Tomamae-cho CC with the theoretically constructed model
having the constant event probability through turnovers.
Table 5 shows the observed data in Tomamae-cho CC in terms of the volume oftransactions and the number of currency notes issued or used in C, C, NC, and NC ateach turnover, and currency velocity calculated from the observed data. The maximum
turnover of the currency is 4, which means that all currency notes were converted into
yen after turnover 4. Table 6 shows the calculated values of Pc, Pnc, Pcy by using the real
data in the Tomamae-cho CC20). Table 7 shows the observed values of C/C, NC/NC,C/X, and NC/X and also their calculated values by using a Pc, Pnc, Pcy , and Pny in Table
6. Table 8 shows event probabilities of C, NC, and Y at each turnover and the average
probability through all turnovers21).
According to Table 5, the circulation velocity of CC in the total transactions X is 5.07,
which is larger than that of any of other transactions, C, C, NC, and NC. This indicates
19)

Thickness of arrows visually symbolizes how large the numbers of currency notes through thecirculation paths are. The dotted lines show the possible circulation paths that the currency notes did
not flow.
20)

Pcy and Pny signify the probability of conversion after the commercial/ non-commercial transactions
by specific business partners. Pc and Pnc are thought of as the ratios of the number of currency notes
flowing in the commercial/non-commercial transactions at turnover 1 and the number of currency
notes converted in yen after the transactions at turnover 1. These are calculated as Pcy1756/2013 andPny8/180.
21)
Turnover 5 is added to enable the currency notes accepted at turnover 4 to be converted into yen.

– 291 –

N. KICHIJI and M. NISHIBE

Fig. 18.

The Tomamae-cho CC circulation tree diagram based on the real data.

that CC in DTS has higher circulation efficiency than legal tender and Eco-money.
According to Table 7, the observed value of C/C (1.080) is higher than the calculatedone (1.009) and the observed value of NC/NC (1) is lower than the calculated one(1.221). All non-commercial transactions have been done at turnover 1. This
concentration of non-commercial transactions makes transaction complementarity effectwork more for commercial transactions, but work nothing for non-commercial– 292 –

Network Analyses of the Circulation Flow of Community Currency

Table 5.

The commercial and non-commercial transaction of CC.

Total: X
Remaining commercial
removing NC: C
Remaining non-commercial
removing C: NC
Commercial only: C
Non-commercial only: NC
CNC
CC

Total: X
Remaining commercial
removing NC: C
Remaining non-commercial
removing C: NC
Commercial only: C
Non-commercial only: NC
CNC
CC

Table 6.

Volume oftransaction

Currencies
issued/used

Circulation ofvelocity

Circulation ofvelocity p.a.

2771

2192

1.264145.07046

2400

2012

1.192844.78448

180
2591
180
2771
191

180
2184
180
2364
172

1.00000
1.186361.00000
1.172171.110474.01099
4.758464.010994.701544.45406

T1
1764

T2
314

T3
77

T4
37

1756

160

60

36

180
1910
180
2090
154

0
177
0
177
17

0
61
0
61
1

0
36
0
36
0

The caluculated value of Pc, Pnc, Pcy, Pny.

Prob. of commercial transaction
Prob. of non-commercial transaction
Prob. of conversion after commercial transaction
Prob. of conversion after non-commercial transaction

Table 7.

PcObservedC/X
PncObserved NC/X
ObservedPcy
ObservedPny

0.93504
0.06496
0.87276
0.04444

The observed and caluculated values of growth rates of C and NC.

DTS growth effect (C)DTS growth effect (NC)Rate. of C to X
Rate. of NCto X

ObservedC/C
ObservedNC/NC
ObservedC/X
Observed NC/X

1.07958
1.00000
0.866110.06496– 293 –

CalculatedC/C
CalculatedNC/NC
CalculatedC/X
CalculatedNC/X

1.008801.22053
0.92689
0.05322

N. KICHIJI and M. NISHIBE

Table 8.

Event probabilities at each turnover of Tomamae-cho CC.

Turnover

1

2

3

4

5

Total

Ratio

Commercial: C
Non-commercial: NC
Converted: Y
Total

0.91788
0.082120.00000
1

0.195260.00000
0.8047410.266360.00000
0.7336410.324560.00000
0.6754410.00000
0.00000
1.00000
1

1.70406
0.082123.2138350.340810.016420.64277
1

Table 9.

Event probabilities at each turnover (reconstructed).

Turnover

1

2

3

4

5

Total

Ratio

Commercial: C
Non-commercial: NC
Converted: Y
Total

0.93504
0.064960.0000010.169280.01176
0.8189610.169280.01176
0.8189610.169280.01176
0.8189610.00000
0.00000
1.00000
1

1.44289
0.10024
3.4568750.28858
0.02005
0.691371transactions. This bias is also seen from Table 8 because each event probability is notconstant through turnovers. The probability of non-commercial transactions drops to andstays at 0 through turnovers 2 to 4, probability of commercial transactions continues toincrease after a big drop at turnover 2, and probability of conversion continues todecrease through turnovers 2 to 4.
Figure 19 is the circulation tree diagram of Tomamae-cho, which we reconstructedassuming that Pc, Pnc, Pyc, and Pyn are constant through turnovers 2 to 4 as in Table 922).
Figures 18 and 19 are similar in terms of the volume of total transactions (X),commercial transactions (C), and non-commercial transactions (NC ) seen in Table 10.
The currency notes circulate through all the possible branching paths in Fig. 19, though
there are only two circulation paths (c–c–c–c and nc–c–c–c) in Fig. 18. However, theseare still the two major paths with largest and second largest volumes of circular flow of
the currency notes. There exist two other intermediate paths such as c–nc–c–c andnc–nc–c–c seen in Fig. 19.
Table 10 shows that C/C is 1.084 and NC/NC is 1.154, These are greater than theobserved and calculated values excluding the calculated NC/NC in Table 7 (observed
C/C1.080, calculated C/C1.009, observed NC/NC1, and calculated

22)

The probability of conversion at turnover 1 is 0 because conversion of unused currency notes is
prohibited by the rule of the system.

– 294 –

Network Analyses of the Circulation Flow of Community Currency

Fig. 19. The Tomamae-cho CC circulation tree diagram reconstructed assuming theconstant event probability.

NC/NC1.221). Constant probability of events equates the transaction complementarity
effects between commercial and non-commercial transactions. This effect is also visible
as the increase of circulation velocity of the currency notes in Table 11. Thus, we canconclude that DTS’s effectiveness is theoretically and empirically demonstrated.
9.

Importance of Dual Directional Transaction in DTS

We can also evaluate the significance of non-commercial transactions for the smooth– 295 –

N. KICHIJI and M. NISHIBE

Table 10.

The caluculated values of major variables (reconstructed).

Number of notes: Z
Total transaction: X
Number of notes used for
C: Zc
Commercial transaction: C
Number of notes used for
NC: Znc
Non-commercial transaction:
NC
Number of notes used for C
and NC: ZcZnc
Difference between NC and
Z: ZcZncZ
Number of notes Removing
NC: ZcRemaining C removing
NC: C
Number of notes Removing :C: Znc
Remaining NC removing
C: NC
C/C
NC/NC

Table 11.

T1

T2

T3

T4

Total

1795.15388
1795.15388
1908.28493

324.99993
649.99986
242.52260

58.83894
176.51683
30.96139

13.00724
52.02898
3.451442192
2673.69955
2185.22035

1908.28493
150.26784

485.04519
10.57219

92.88417
0.7103613.80575
0.03405

2500.02004
161.58444

150.26784

21.14438

2.13108

0.13621173.67951

2058.55277

253.09479

31.67175

3.485492346.80479

263.39889

71.90514 27.16719

9.52175

154.80479

1789.69038

213.03389

25.55919

3.451442031.73491

1789.69038

426.06779

76.67758

13.80575

2306.24150

132.37413
132.37413

8.22442
16.44884

0.51455
1.54366

0.034050.13621141.14716
150.50284

1.06627
1.13518

1.138421.28546

1.21136
1.380531
11.08402
1.15399

The circulation velocity of currency notes.
In 91days of experiment period

Per annum

1.21975
1.14406
1.135111.07485
1.06628

4.892424.588814.55291
4.311224.27685

Circulation velocity (v)Circulation velocity in C (C/Zc)
Circulation velocity after removing NC (C/Zc)Circulation velocity in NC (NC/Znc)
Circulation velocity after removing C (NC/Znc)circulation of Tomamae-cho CC from a different angle because non-commercial
transactions increase the reciprocity of total transactions. We employ “triad census” as an
estimation method and use Pajek1.1.1. We can confirm how the non-commercial
transactions helped smoothen the total transactions. The triad censuses for the total– 296 –

Network Analyses of the Circulation Flow of Community Currency

Fig. 20.

Types of Triad.

transactions and for the commercial transactions data in Table 12 show many of the main
findings. Figure 20 shows the types of triad. The Z scores in Table 12 indicate thedeviations of the observed values from those expected by random digraph distribution(Wasserman and Faust, 1994; Kanamitsu, 2003). In the total transactions, the Z scores of
3-102, 5-021U, 9-030T, 7-111D, and 8-111U were greater than 1; this result shows thecharacteristics of the TCCN. However, in the commercial transactions, the Z scores of 3102, 7-111D, and 8-111U were less than 0; the characteristics of the TCCN in the totaltransactions disappeared. 3-102 represented a two-way exchange between two people
and specific business partners or cooperative groups. The vanished 3-102 means that theflow of CC altered from a two-way exchange to a one-way exchange. 7-111D and 8111U were the same as 3-102. This result indicates that the non-commercial transactions
facilitated two-way exchanges within Tomamae-cho CC. In the commercial transactions,since receivers were limited to the specific business partners, Tomamae-cho CC
accumulated at the specific business partners and could not flow smoothly unless these
specific trading partners were willing to make purchases from other participants with– 297 –

N. KICHIJI and M. NISHIBE

Table 12.

Triad censuses for TCCN.

Total transactions in Feb. 2005

Commercial transactions in Feb. 2005

Triad type

Frequency

Z23)

Triad type

Frequency

Z

3-102
16-300
1-003
4-021D5-021U
9-030T
12-120D
13-120U
2-012
14-120C
15-2106-021C
7-111D
8-111U
10-030C
11-201380
01576575
106
1135
31
1
1
54851
0
0
231
37
7
0
0

1.21
1
0
0.38
5.59
13.92
158.51158.51
0.04
1
1
0.33
16.81
2.37
1
1

3-102
16–300
1-003
4-021D5-021U
9-030T
12-120D
13-120U
2–012
14-120C
15-2106-021C
7-111D
8-111U
10-030C
11-201

0
0
64855
26
207
2
0
0
5194
0
0
16
0
0
0
0

1
1
0
0.29
4.68
1
1
1
0.02
1
1
0.78
1
1
1
1

Tomamae-cho CC. Therefore, the non-commercial transactions are crucial for bothcommunity revitalization and economic activation. Tomamae-cho CC used in the noncommercial transactions are going to be absorbed by the commercial transactions in duetime, and Tomamae-cho CC that are purchased for social welfare or volunteer activities
are expected to put a brake on the spillover of purchasing power to other towns.
10.

Concluding Remarks

CC is a “socio-cultural medium,” which activates local economies and reinforces
cooperation of communities and mutual aid. Our network analysis empirically showsthat the aspects of the socio-cultural medium functioning successfully within thecommunity help the aspects of the “economic medium” to act properly. We obtained fourmain results in this study: (1) various distributions of Tomamae-cho CC obey a powerlaw distribution; (2) the networks of the Tomamae-cho CC display the characteristics ofa small-world networks similar to those of organisms; (3) directional and weighted
network analyses are important because the directional graph often shows asymmetry of
23)

The Z score is the value of (frequency–expected frequency)/expected frequency.

– 298 –

Network Analyses of the Circulation Flow of Community Currency

the network, and the correlation coefficient between degree and weight is significantly
less than 1; and (4) DTS is effective in the sense that it can increase the volumes of bothcommercial and non-commercial transactions by its “transaction complementarity
effect” or “currency crossover effect,” and that it can enhance dual directionality andreciprocity of transactions. We conclude that network analyses and currency circulation
path analysis are both necessary to understand the flow of CC. The information acquired
from our network analyses might provide relevant direction to researchers and decisionmakers for addressing regional policies and planning.
Acknowledgments
We would like to express our appreciation to the Tomamae-cho Commerce and Industry
Association and to the Tomamae-cho municipal government for their support and cooperation in
our research and to LETS-Q for permitting us to use its transaction data for our research; and to
Takayoshi Kusago, Ippei Hozumi, Kenichi Kurita, Kenichi Yamamoto, Masayuki Yoshida, andSatoshi Yoshii for their collaborations in the Tomamae-cho CC experiment. We would also liketo thank Satoshi Tanda, Kazuo Machino, and Victor M. Yakovenko for their advices andcomments. This work was supported by Hokkaido University’s 21st Century COE program“Topological Science and Technology.” We are grateful to the referee of this paper forcomments and criticism.

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