Discussion Paper No.307
An economic geographical analysis of relevancies
between the city systems
Toshiharu Ishikawa
Faculty of Economics
Chuo University
February 2019

INSTITUTE OF ECONOMIC RESEARCH
Chuo University
Tokyo, JapanAn economic geographical analysis of relevancies between the city systems

Toshiharu Ishikawa

1 Introduction
Cities are places where production and consumption activities are linked and realized in region. And
these economic activities are conducted by people who live in city and city areas. It is said that thecities are places that represent the human economic activities in region. Thus, the cities are gaining
attention and have been analyzed in many academic disciplines. Economic geography is one of aleading academic field in the analyses and it has been studied the cities for the past two centuries.
From the viewpoint of economic geography, the changes in economic activities of the cities isoutlined as follows. At the stage of early economic development where economic activity in generalis substantially limited within a territory of the country, the formation of the individual cities, theirindustrial composition, and the optimal population size of the cities are analyzed. As the relationships
and cooperativeness between the cities are gradually formed, and a concept of city system in a regionis established. The structure of city system attracts attention of the scholars in the regional economics.
In the analysis of city system, the market areas of retailers are analyzed in detail since the market areas
are the basis of building city system.
In the following stage of economic development, through the progress of the various kinds oftechnologies the economic globalization advances. The globalized economy generates a harsher pricecompetition in the manufacturing industry in the industrial countries. Especially, the manufacturingfirms in existing industrial areas are exposed to the price competition which is followed by a cost
cutting competition. In order to cope with the cost cutting competition, many manufacturing firms
fragment production processes to reduce production costs. Some fragmented processes are scattered
to other local cities where the factories produce goods with the lower costs. In addition to this,production activities of the manufacturing firms are supervised by the management functions which
are organized through the interconnected cities and the city systems. The relationships between thecity systems, therefore, are deepen through the firms’ managements The importance of thecoordination between the cities increases in firms’ production and sales activities. In the era when theeconomic activity is globalized, the relevancies between the city systems inevitably expands anddeepens. Fragmentation of firms’ production processes and the spatial diffusion of the fragmented
processes change the economic role of the cities and vary the spatial economic structure of city systems.
Tracing the transition of the cities, it seems that establishing a broad framework to analyze the city1

systems is required in the field of Economic geography 1. Ishikawa (2016) examines the theories of
construction of city systems which have been basic economic unit in the globalization economy. And
he proposes construction method that can make the existing analysis framework of city system
diversified and increases their applicability. This paper focuses on the relevancies between city
systems from the view point of the empirical analysis. And the present paper, applying the network
analysis and graphical modeling method, analyze how the relevancies between the city systems areformed by using industrial data in Japan.
The paper is organized as follows. In the next section, a method to quantify the characteristics ofcity system is explained by using a case study of the city system in Yamagata prefecture in Japan.
Section 2 analyzes the level of relevancies between the city systems by the data of the passenger flow
amounts of the prefectures in Japan. Subsequently, Section 3 the relevancies between the city systems
is examined by using location data of the branch factories and business/sales offices of companies inmanufacturing industry. By combining the indicator showing the characteristics of the city system andthree indicators indicating relevancies of the prefecture, the followings will be found out: 47
prefectures in Japan are divided into 16 groups and there is a possibility that their economic
geographical characteristics can be explained successfully from the relevancies between prefectures .
Section 4 summarizes the results obtained in this paper.

2 Qualification of city system
2.1 City system in Yamagata prefecture
Let us select the city system in Yamagata prefecture in Japan to describe a city system in a region.
Fig.1 depicts the distribution of city population in Yamagata Prefecture in 1969, ranking the cities
according to population size. Fig.1 shows the regularity in the distribution; the distribution of city
population is formed by three stratums and the series of the number of cities in each stratum is 1-3-9.
These regularities are successfully explained by the concept of the city system according toChristaller’s theory (1933) using the market areas of the retailers under the pseudo-monopoly.
Fig.2 shows the city population distribution in Yamagata prefecture in japan in 2015. The
distribution of city population is polarized; one large city and many small cities. As indicated by thecomparison between Fig.1 and Fig.2, the second stratum of the city population distribution collapses
in 2015, and the city population distribution has become more concentrated. It seems to be difficult to
explain and interpret such the change of the city system by the traditional city system theories basedon Christaller and Lӧsch (1942). Ishikawa (2016) proposes the concept of Flexible Market Area
Theory which deals with this change of the city system.

1

A lot of theoretical studies on city systems have been accumulated so far. Useful inconsideration here are as follows. Beckmann-McPherson (1970), Capello (2004), Hoover (1970).
Parr (1988), and Tinbergen (1968).
2

City population
200000180000160000140000120000100000
80000
60000
40000
20000
0

0

2

4

6

8

10

12

14

Rank

Fig.1 City population distribution in Yamagata prefectute,1969

City population
300000250000200000150000100000
50000
0

0

2

4

6

8

10

12

14

Rank

Fig.2 Population distribution of cities in Yamagata prefectute,2015
2.2 Derivation of an index to describe city system
As shown in the previous subsection, over time the city system changes and shows different aspects.
And it could be said that city system established in regions show various characteristics. Since the city
system is formed on the basis of people's economic activities, economic principles should play a majorrole in the formation of city systems and their characteristics. Therefore, it is inferred that differencesin structures of the city systems are related to the industrial characteristics of the region.
For the purpose of verifying the relationships between city system and regional industrial
characteristics from empirical analysis, an index to describe city system is needed. Thus, the City
3

System Index is devised as an indicator to show the characteristics of city systems. The City System
Index captures a city system from two points of view, the distribution of city population and the densityof cities in a region. In this subsection, after explanation of method of derivation of the City System
Index, the City System Index is concretely derived using Japanese data and the index is used to show
characteristics of the city systems in Japan.

2.3. Derivation of City System Index
2.3.1 Divergence of city population distribution to the largest city
In order to describe the divergence toward the primary city of the population distribution of the cities
which form a city system, the coefficient of the divergence is used. Based on the framework shown by
Sheppard (1982), the coefficient of the divergence, CD, is derived as follows (Sheppard, 1982).
Suppose that there are N cities in a region. Term of p r denotes the population share of a city for all
cities’ population in the region. The value of CD obtained by equation (1) is considered as thecoefficient of divergence of the population distribution to the primary city in the region.

∑ p L (r)CD = (1/N)

N

r =1 r N(1)

where r is rank of city by population share order.
CD is used as the index that indicates the characteristic of the distribution of cities’ population in acity system. As the distribution of cities’ population becomes to diverge toward the largest city of thecity system, the value of CD lowers.

2.3.2 Spatial convergence of city distribution in a region
A city system is captured from the viewpoint of the locations of the cities within a city system; thespatial convergence of the cities’ locations in a region. The spatial convergence of the cities’ locations,SC, in a region is derived by using Poisson distribution. Assume that there are N i (i=1, 2, 3…N) cities
in a region of which land area is M. The distance from a city N 1 to the nearest city is denoted as d 1 .
This distance is named as the least distance of the city N 1 . The least distance is obtained for each of
cities N i (i=1, 2, 3…N), the average least distance, AD, of cities is derived as equation (2),AD = (1/N)∑i=1 d i
N(2)The spatial convergence of cities distribution in region, SC, is expressed by equation (3),SC=AD/(1/(2 (N/M)0.5 ) )(3)

As the cities locate more closely each other, SC becomes smaller. The SC’s value is used to specify aspatial characteristic of a city system.
42.3.3 Derivation of the City System Index for 47 prefectures in JapanThe values of both CD and SC become smaller as the divergence of the distribution of cities’
population to the largest city progresses and the spatial convergence of cities distribution is higher.
Hence, combining these two values, an index can be built to reveal the characteristics of city systems,
City System Index, CSI. The City System Index is derived by equation (4),CSI＝( ( α CD )2 + ( β SC )2 )0.5

(4)where α and β are positive parameters. When the value of the CSI is lower, it means that the structureof the city system has concentrating characteristics in terms of the cities’ population distribution andthe location of cities. On the other hand, the high value of the CSI means that the structure of the city
system has leveling characteristics. In the rest of this chapter, CSI is used as an index that indicatesthe characteristics of city systems.
Let us derive the CSIs of the city system in Yamagata prefecture in 1964 and 2015. The parametersin the equation (4) are assumed as α＝20 and β＝1. The CSI in 1964 can be derived as 2.52 and thatof 2015 is 2.32. As shown by comparison of Fig.1 and Fig.2, City system in Yamagata prefecture in2015 becomes concentrating more than that in 1964 since the divergence of the population distribution
to the primary city becomes higher in the period between 1964 and 2015.
City System Indices of 47 city systems in 47 prefectures in Japan in 2012 are shown in Table 1. In
Table 1 the standardized CSI of each city system is also shown to derive the relative differences in thecity systems of 47 prefectures. And locations of 47 prefectures are indicated by the number assigned
to each of all prefectures in Fig.3

Table 1 City system Indices of 47 prefectures in Japan,2012
Prefecture

No. CSI

Standardized

Prefecture

No.

CSI

CSI

Standardized
CSI

Hokkaido

1 1.5325-1.4569Mie

24

2.76430.1934

Aomori

2 3.0892

0.6341Shiga

25

2.6756-0.0702Iwate

3 3.2298

0.8076

Kiyoto26

2.2535-0.5842

Miyagi4 2.3012-0.4266

Osaka

27

1.2892-1.5093Akita

5 3.151

0.7066

Hiyogo28

2.2265-0.5194

Yamagata

6 2.3449-0.3772

Nara

29

2.2103-0.5562

Fukushima

7 2.7192

0.1399Wakayama

30

4.36672.3597

Ibaragi

8 1.9486-0.9003

Tottori31

4.2606

2.1984

Tochigi

9 2.1339-0.6218

Shimane32

3.75091.4544Gunma

10 2.5702-0.0725

Okayama

33

2.75740.1745

Saitama

11 1.6851-1.3954

Hiroshima34

2.5905-0.03835Chiba12 2.1704-0.7022

Yamanashi

35

3.646

1.3784Tokyo

13 1.2008-1.9211Tokushima

36

4.1194

1.9851

Kanagawa

14 1.8164-1.0735

Kagawa37

2.3134-0.4295

Niigata

15 2.143-0.6464

Ehime

38

2.536

-0.1298

Toyama16 1.9671-0.8928Kochi

39

3.7353

1.4916

Ishikawa

17 3.5271

1.1968

Fukuoka

40

1.7398-1.1872

Fukui

18 3.0731

0.6040

Saga

41

3.039

0.5613

Yamanashi

19 2.3523-0.3783

Nagasaki

42

2.84650.2978Nagano20 2.139-0.4033

Kumamoto

43

3.045

0.4914Gifu

21 2.2844-0.3387

Oita

44

3.21040.7793

Shizuoka

22 2.4623-0.4783

Miyasaki

45

3.344

0.9625Aichi

23 1.5726-1.4110

Kagoshima46

2.89530.3633

Okinawa

47

2.4394-0.2575

Fig.3 Locations of 47 prefectures in Japan

3 Analysis on the relevance of a city system with other city systems
3.1 Framework of the analysis of relevancies between city systems
As mentioned in the above section, people's consumption activity and production activity are
6embodied in cities. Each city is rarely isolated and usually belongs to a city system. As economic
activities expand to cover whole the world, the export and import of products among these city systems
increase and the movements of various kinds of intermediate goods such as machinery parts also
sharply increase. As a result, economic relations among city systems are greatly deepened.
It could be said in Japan that a city system is formed in a prefecture, centering on the city of theprefecture's government. Export and import of goods between the city systems can be regarded as
movements of goods between the prefectures. This section, based on the data of the prefectural
economic activities in Japan, analyzes the relevancies between city systems.
This section is organized by three stages. The first stage focuses on amount of passenger flow
between the prefectures. Based on the distribution of the passenger flow amounts between theprefectures, the relations between the prefectures are processed to be represented by 1 and 0. A network
analysis derives relevance index, NIf, through passenger flow amounts. NIf shows the prefecture’s
relevance to other prefectures based on the amounts of passenger flow. This NIf is considered as anindex that indicates how much a city system in a prefecture has relevance with the city systems inother prefectures. And then, the relationship between NIf and CSI is analyzed for each city system.
The second stage proceeds as follows. First, it picks up the locations of the branch factories andsales offices of companies, which are fixed facilities of the companies. Specifically, it investigates
how branch factories and business/sales offices of 152 companies in the machine assembly industry
are distributed among 47 prefectures in Japan. Using the number of locations of branch factories ofcompanies in each prefecture, correlation matrix and partial correlation matrix are created. And
making use of the graphical modeling method, relativity between prefectures is represented by 1 and
0. Then, summing the relativities of each prefecture to other 46 prefectures provides an index of therelevance index through the locations of the branch factories, NIp. The NIp represents the extent towhich a city system in a prefecture has cooperation with other city systems through the location of
branch factories of the companies. In the same way, an index of relevance index, NIm, based on
business/sales offices is obtained. The NIm shows the extent to which a city system has cooperation
with city systems in other prefectures though the locations of the company's business/sales offices.
In the third stage, the results obtained in the second stage are illustrated in relation with the results
obtained in the first stage. The obtained results are interpreted from the viewpoint of economic
geography. From these three-stage analyses, it is clarified what kind of features the 47 city systems inJapan have and how they are related to other city systems 2.

2

The passenger flow amounts between the 47 prefectures in Japan are provided by Data Books by
Toyo Keizai Shinposha (2016). And Toyo Keizai Shinposha (2017) shows information of firms’
branch factories and sales/business offices.
7

3.2 Relevance between city systems based on passenger flow amount between prefectures
This subsection estimates the relevancies between prefectures based on passenger flow amounts
between prefectures. The estimation procedure of the relevancies is as follows. Passenger flow
amounts between 47 prefectures in Japan are obtained from the data of 2017 and they are displayedby ratio in matrix formed by 47 prefectures 3. There are large differences among the values of the ratiosof the prefectures’ passenger flow amounts. Thus, considerably lower ratios near to 0 are positively
set to 0 in the matrix, while large ratios are set to 1. The prefectures which are set 1 by a prefecture
are judged that they have relevance each other; they are connected through the prefecture, while theprefectures which are set 0 are supposed that they do not have relevance each other.
In addition to prefectures, the following four ratios are incorporated as a criterion for determining
the relevance between prefectures. 1) ratio of [passenger flow amount outside the prefecture /passenger flow amount in the prefecture], 2) ratio of [passenger flow amount outside the prefecture /total passenger flow amount in Japan], 3) ratio of [passenger flow amount outside the prefecture /goods flow amount of the prefecture] , 4) ratio of [GRP of the prefecture / GDP in Japan].

In eachcriterion, considerably lower ratios near to 0 are positively set to 0, while large ratios are set to 1. And
it is judged that the prefectures with the value of 1 in a criterion are connected through the criterion.
A value of 0 or 1 is assigned to individual 47 prefectures based on 51 criteria. This creates a matrix X
by rowing 51 criteria items and associating 47 prefectures with columns.
This subsection derives connectivity among the prefectures using the basic concept of network
analysis theory. According to a theory of network analysis 4, multiplying the matrix X by its transposed
matrix X′forms the matrix X X' which shows the relevancies between the 47 prefectures. The
relevance that each prefecture has with each of the other prefectures is indicated by the X X' matrix.
By summing up the numerical values in each row, Network Index based on based on passenger flow
amounts, NIf, that indicates the level of relevance of a prefecture to outside city systems is obtained.
It is considered that the value of NIf of the prefecture is used as a relevance index of the city systemthat shows the level of connected with other city systems. Table 2 shows the numerical values of NIf
of 47 prefectures which is standardized using the data of the passenger flow amounts in Japan 2016.

Table 2 Relevance indices, NIf, of 47 prefectures in Japan,2016

Prefecture

No. Standardized

Prefecture

No. Standardized
NIf

NIf
Hokkaido

1-0.0192

Mie

24-0.8846

Aomori20.4135Shiga

25-0.3557

3
4

Data Books published by Toyo Keizai Shinposha (2017).
There are many studies on Network analysis. For example, see works shown in Book by Von
Wouter et al (2005).
8

Iwate30.6635

Kiyoto26

1.0384

Miyagi4

1.2596

Osaka

27

1.375

Akita

5

-0.7885

Hiyogo28-0.6346

Yamagata

60.0385Nara

29-0.8173

Fukushima

7-0.2596

Wakayama30-2.2884

Ibaragi

8-0.9712

Tottori

31-1.7307

Tochigi

9-0.7596

Shimane32

0.0576Gunma

10-0.5385

Okayama33

0.1826

Saitama

11-1.3654

Hiroshima

34

1.6538Chiba

12-1.3654

Yamanashi

35-1.8942Tokyo

13

1.6635Tokushima36-1.0384

Kanagawa

14-0.5288

Kagawa37

0.1153

Niigata

15

1.3269Ehime

38-0.3653

Toyama16

0.3462Kochi

39-0.0769

Ishikawa

17

1.7692

Fukuoka

40

0.8846Fukui

18

0.6827Saga

41-1.0192

Yamanashi

19-0.2115

Nagasaki42

0.0288Nagano20

0.9038

Kumamoto

43

0.3365Gifu

21

0.2596Oita

44-0.2692

Shizuoka

22

0.9038Miyasaki45-0.5865

Aichi

23

1.4712

Kagoshima

46

0.6634

Okinawa

47

0.7211

3.3 Analysis of the relationships between city system index and relevance index
This subsection examines the relationships between city system index (CSI) and relevance index (NIf).
Fig.6 shows the city system index CSI, which is standardized, on the horizontal axis and the relevanceindex through the passenger flow amounts, NIf, which is standardized, on the vertical axis. These
values of each of 47 prefectures are indicated by coordinate points. Fig.6 is divided into the four
quadrants, A, B, C and D which are assigned in the counterclockwise direction from the upper left of
the figure. The characteristics of the prefectures in each quadrant can be inferred from the economic
geographical viewpoint.
(1)The city systems in the prefectures belonging into the quadrant A are intensive and they havehigh relevancies with the city systems in other prefectures. The prefectures that play important socialand economic roles in Japan such as Tokyo (No.13), Aichi (No.23), Osaka (No.27) are located in the
North-West part in the quadrant A. And the prefectures that play social and economic roles in a regional
9

level are also placed in the quadrant A; Miyagi (4), Niigata (15), Kyoto (26), Hiroshima (34), Fukuoka(40), Okinawa (47) are also in this quadrant. It is clear that the prefectures that play social andeconomic roles in the whole country or in the regional areas are placed on this quadrant: And thestructure of city systems in these prefectures are intensive and based on the passenger flow amounts,
they have high relevancies with other city systems.

13
27
22

A

23

40

26

15 4

2

2
47
1
8

21
37

1
-3
19
25
38
14

8

34

17

NIf

4
18

3

1.5
1

43
33
42
32

0.5
-2

-1

0
-0.5

0

1

CSI

2

3 39
44
9
5 45

-1
-1.5

28

36

-2

C

-2.5

B
11

1

29

D

2

31

9 12 24
41

35

30

Fig.4 Relationship between CSI and NIf of 47prefectures in Japan(2)The city systems of the prefectures in the quadrant B are intensive and they have low relevancies
with the city systems of other prefectures. Prefectures in the quadrant B are Saitama (11), Chiba (12),Ibaraki (8), Tochigi (9), Gunma (10), Kanagawa (14), Hyogo (28), Nara (29), Shiga (25), andYamanashi (19). These prefectures are located around the regions which play large social-economicroles in Japan. The economic scale of these prefectures is large, but, the values of NIf of them are low
since their connectivity of these prefectures is considered to be biased toward Tokyo or Osaka region.
Therefore, it can be said that based on the passenger flow amounts, in prefectures adjacent to theregions that play huge social-economic roles, their city systems have intensive structure and have low
relevance index . It is clear that in the quadrant B the geographical location of the prefecture decisively
influences the spatial economic characteristics of its city system.
(3)The prefectures in the quadrant C and D are located relatively departed from the regions which
10play central role in social-economic activity and their city system are leveled. And almost prefecturesin this quadrant have low relevancies with the other prefectures.
A typical characteristic of the prefectures in the quadrant C may be successfully explained by theindustrial composition and geographical situation of the two prefectures, Wakayama (30) andYamaguchi (35). They are located in the lower right part of the quadrant C. They have a large
proportion of heavy chemical industry in its industrial composition 5. It could be considered that
because dominant parts of production activity are carried out by many equipment machines, theirrelevance index based on passenger flow amounts is low. In addition to this, Yamaguchi Prefecture
is sandwiched between Hiroshima and Fukuoka prefecture, which possess large economic scale. Thus,
large city is hard to be formed in Yamaguchi prefecture and its city system is thought to be leveled.
And although Wakayama prefecture is adjacent to Osaka, its geographical shape is complicated andquite long, so its city system becomes level. While, Tottori (31) is explained from rather different
viewpoint. It is departed far from Osaka in time and the economic scale is quite small: Since Tottoriis rather isolated from other prefectures, its city system is leveled and the relevance through thepassenger flow amounts is low. In sum, it could be considered that the city systems of prefectures inwhich the economic scale is rather small and the ration of heavy industries in the industrial
composition is high, tend to be leveled and to have low relevance index based on passenger flow
amounts.
(4)The city systems of the prefectures in the quadrant D are level and they have relatively highrelevance with the city systems of other prefectures. Typical characteristics of the prefecture belonging
to this quadrant are shown in Ishikawa Prefecture (17). Ishikawa Prefecture is relatively far from
Tokyo and Osaka and faces the Sea of Japan. Although the economic scale is not so high, theproduction value of the production equipment is considerably high, and the production machine
occupies the first rank in its industrial composition. Prefecture is not in Japan other than Ishikawa
prefecture where production machine occupies the top position in the industrial composition. It could
be said that in the prefectures, in which economic scale is small and the non-equipment industry is
popular in industrial composition, the city systems are leveled and have high relevance index basedon passenger flow amounts.
In order to show typical characteristics of the four quadrants, let us expand slightly the scope ofanalysis: First, select three prefectures from each of the four quadrants, and choose the following items
as criterion; ratios of population and GRP of each prefecture in Japan, and the top three industries that
account for the high proportion of each prefecture's industrial composition. By these simple
5

The analysis here does not focus on heavy chemical industry. The analysis of this paper covers
companies belonging to industries with relatively many factories and branches. Nevertheless,
Considering the characters that fundamental industries may have, the result derived here may be
judged to be valid.
11

procedures a fundamental characteristic of the four quadrants is derived. Table 3 shows a characteristicof the three prefectures in each quadrant from the three criteria. Table 3 may describe successfully atypical characteristic of the prefectures in each quadrant in Fig.4.

Table 3 Characteristics of representative 3 prefectures in each dimension,2012
Pref. pop. GRP

business typeshipment value business typeshipment value business typeshipment valueNo.

rank 1(1million yen)

(1million yen)

(1million yen)%%rank 2

rank 3A 13

1018.3 transportation

1,473,415 printing

1,014,133 IT equipment

832,955

A 23

5.73

12.8 transportation

23,091,312 steel

2,437,217 electric equipment

1,894,771

A 27

6.85

13.1 chemistry

1,987,514 oil-coal products

1,660,105 metal product

1,354,280

B8

2.34

4.36 chemistry

1,511,568 groceries

1,164,414 product equipment

1,031,433

B 11

5.64

8.1 transportation

1,820,269 chemistry

1,636,801 groceries

1,507,802

B 12

4.85

7.71 oil-coal products

3,062,973 chemistry

3,016,494 steel

1,697,053

C 29

0.8

1.34 steel

846,093 oil-coal products

825,772 chemistry323,057

C 31

0.46

0.68 device

139,067 groceries

131,312 pulp-paper

91,465C 35

1.14

2.11 oil-coal products

1,95,9488 chemistry

1,610,271 transportation

1,015,623

D3

1.04

1.63 transportation

669,404 groceries

320,842 device

211,958

D 17

0.91

1.66 product equipment593,255 device

313,773 fabric

192,991

D 18

0.63

1.15 chemistry289,475 device

257,038 fabric

234,708

3.4 Relevance Indices based on branch factories and business/sales offices
This subsection focuses on manufacturing companies have some branch factories and business/sales
offices. And 152 manufacturing companies are arbitrarily extracted. Then, using the numbers oflocations of branch factories and business/sales office in every prefecture, the two kinds of indices of
relevance of every prefecture with other prefectures in Japan are derived. The obtained relevanceindices of prefecture are used as those of the city system within the prefecture.

3.4.1 Relevance index of city system through locations of branch factories
Procedure for deriving the relevance index of a city system through companies’ branch factory
locations is as follows. First, 152 companies are extracted from the industry data of 2016. The
headquarters, which is handled as one factory, and locations of the branch factories of each company
in every prefecture are examined. Then, the number of the factories is assigned to the 47 prefectures.
0 is assign to prefectures where branch factory is not located. The latter two steps are carried out forevery company. As a result, a correlation matrix of 47 rows and 47 columns is derived based on thelocations of the factories of the 152 companies. Each element of this matrix reveals the level of12relevance between the prefectures through the branch factory. From the correlation matrix, a partial
correlation matrix is derived. An element close to zero in the partial correlation matrix is positively set
to 0, and from this matrix a correlation matrix is estimated. The same procedure is carried out
iteratively until the simplest correlation matrix is obtained. In the resulted correlation matrix, 1 isassigned to nonzero elements. This creates the matrix of 47 rows and 47 columns consisting of 1s and
0s. The prefectures assigned 1 in an element of the matrix have a connectivity each other through thelocation of the branch factory of a company. And the value obtained by summing up elements of eachprefecture is considered as the degree of the relevance to others, which is denoted by NIp. This NIp isused as the level of relevance of a city system in a prefecture to other city systems. Table 4 shows thevalues of standardized NIp of 47 prefectures in Japan.

Table 4 Relevance Index, NIp, of 47 prefectures in Japan,2016

Prefecture

No. Standardized

Prefecture

No. Standardized
NIp

NIp
Hokkaido

10.4519Mie

240.5916

Aomori20.0188Shiga

25-1.0197Iwate

3-1.7135

Kiyoto26

0.4125

Miyagi40.0188Osaka

27-1.1988Akita

5

0.4519Hiyogo28-0.4826

Yamagata

60.0188Nara

29-2.2730

Fukushima

70.4519Wakayama

30

0.2335

Ibaragi

8-0.8473

Tottori

31

1.6658

Tochigi

9-0.8473

Shimane32

1.4868Gunma

100.4519Okayama

33-0.1245

Saitama

110.4519Hiroshima34-1.0197Chiba

12-0.8473

Yamanashi

35-0.1245Tokyo

13

1.7511Tokushima

36

1.4868Kanagawa

141.3181

Kagawa37

0.4125

Niigata15

1.3181

Ehime

38-0.3036

Toyama16

2.1842Kochi

39-1.9150

Ishikawa

17-1.7135

Fukuoka

40-1.0197

Fukui

18

0.0188Saga

410.2335

Yamanashi

19-0.4142

Nagasaki42

0.7706

Nagano20-1.2804

Kumamoto

43

0.9497Gifu

210.0188Oita

44

1.665813

Shizuoka

22-0.4142

Miyasaki45

0.2335Aichi

23

0.8850Kagoshima46

2.0239Okinawa47-1.0197

3.4.2 Derivation of relevance index based on the locations of business/sales offices
This subsection inquires the locations of the business/sales offices of manufacturing companies. And
152 companies are extracted from the data of 2017, and then, the locations of headquarters andbusiness /sales offices of each company are examined. The headquarters is treated as one business/sales office and the number of locations of business/sales offices in prefecture is assigned to theprefecture. While, prefectures where the office is not located are assigned 0. The same procedure is
carried out for the 152 companies. The procedure for deriving relevance index of the city systemthrough the location of the business/sales offices is the same as the index through the branch factories
mentioned above. The prefectures assigned 1 in an element of the matrix have a relevance each otherthrough the location of the business/sales offices. The value obtained by summing up the elements ofeach prefecture is considered as the degree of the relevance to other prefectures, which is denoted by
NIm. This NIm is used as the level of relevance of a city system in a prefecture to other city systems
in other prefectures through the location of the business/sales offices. Table 5 shows the values ofstandardized NIm of 47 prefectures in Japan.

Table 5 Relevance Index, NIm, of 47 prefectures in Japan,2016
Prefecture

No. Standardized

Prefecture

No. Standardized

NIm

NIm

Hokkaido

1-0.6617Mie

24-0.4142

Aomori20.0544Shiga

25-0.8473

Iwate

3-0.6617

Kiyoto26-0.8473

Miyagi4-0.8407Osaka

27

1.3181Akita

50.2335

Hiyogo28

2.6173

Yamagata

6

1.1287Nara

29

0.0188

Fukushima

7

1.1287

Wakayama

30-0.8473

Ibaragi

8-0.1245

Tottori

31

0.0188

Tochigi

9-0.1245

Shimane32-0.8473Gunma

10-0.1245

Okayama

33-0.8473

Saitama

11-0.8407

Hiroshima

34

0.4519Chiba

120.0544

Yamanashi

35

1.7511Tokyo

13-0.6617

Tokushima

36

0.451914

Kanagawa14-1.0197

Kagawa37

0.4519Niigata15-0.3036

Ehime

38-1.2804

Toyama16

1.3077Kochi

39-0.8473

Ishikawa

17-1.0197

Fukuoka

40

0.0188Fukui

18

0.4125Saga41-0.4142

Yamanashi

19-0.8407

Nagasaki42

1.3181Nagano20-0.1245

Kumamoto

43-0.8473Gifu

21

1.8449Oita

44-0.4142

Shizuoka

22-0.6617

Miyasaki45-0.4142

Aichi

23-0.4826

Kagoshima46-0.8473

Okinawa

47

0.01883.4.3 Characteristics of relevancies between city systems from economic geographical viewLet's combine two kinds of the relevance indices which are derived the above two subsections for eachof prefectures placed in each quadrant of A, B, C, D: By the examination of these combinations thissubsection observes characteristics of relevancies between the city systems in these four quadrants
from an economic geographical view.
(1)In Fig.5 NIp is measured on the horizontal axis and NIm is indicated by the vertical axis. The
diamond marks of the figure show the combination of the two relevance indices of each prefecture in
the quadrant A. From Fig.5 the followings are indicated. Of 14 prefectures 11 ones in the quadrant A
have relatively high relevance with others through the branch factories in manufacturing industry. It
is said that the city system of the prefectures which play central roles in social and economic activities
in the country have intensive structure and they have high relevancies in NIf and NIp and low
relevance in NIm: The networks of the prefectures through branch factories are rather wide, while the
networks through business/sales offices tend to be narrow.
(2)Fig.6 shows the combination of the two relevance indices in each prefecture belonging to thequadrant B. The number of prefectures in the quadrant B is 12. The city systems of these prefectures
have intensive structure. And almost all prefectures located in the vicinity of the prefectures withhuge social and economic activities are placed in the South area of Fig.6. That is, 11prefectures of 12
ones in the quadrant B have relatively low relevance indicated though the business/sales offices. Only
one, Chiba Prefecture (12), is slightly away from the South area. As can be easily expected, these
prefectures are thought to have a great influence on proximity to regions with huge economic activity

15

A

NIm

26

21

2

6
16

1.5

37…

1
0.5

-3

-2

0

-1

NIp
0

1

2

3

15
23

-0.5

4

-1

27

-1.5
20

13

47

22

40

34

Fig.5 Combination of two relevance indices in quadrant A

NIm

B

2

1.5
1
0.5
12
8

-2

-1

9

0
-0.5

NIp
0

1

2

10
28

-1

38

3

1

-1.5
14

-2
25

19

-2.5
29

11

Fig.6 Combination of two relevance indices in quadrant B

16

(3)Fig.7 shows the combination of the two relevance indices NIp and NIm of each prefecture
belonging to the quadrant C. The number of prefectures belonging to the quadrant C is 11. The city
systems of these prefectures have level structure. And the prefectures in this quadrant are relatively
far from the prefectures with large social and economic activities. And 82 percent of the prefecturesin this quadrant belong to the North area of Fig.7. That is, their relevancy index based on NIm is high.
Only two prefectures of Kochi (39) and Yamaguchi (35) enter into the South area of Fig.7. Many
prefectures in this group are considered to substitute for the passenger flow amounts with the locationsof the business/sales offices. Kochi (39) prefecture seem to have different economic geographicalcharacters from others.
44

31

NIm

36

7

2

32

C

1.5

24

5

1

45
41

0.5
30
-1

-0.5

0
-0.5

35
0

0.5

1

1.5

2

NIp

-1
-1.5
39

-2
-2.5

Fig.7 Combination of two relevance indices in quadrant C(4)Fig.8 shows the combination of the two relevance indices of each prefecture in the quadrant
D. The number of prefectures in the quadrant D is 9. The city systems of these prefectures havelevel structure. The prefectures that in this area are relatively far from the prefectures that play
central roles in social and economic fields. And 67 percent of the prefectures in the quadrant D
belongs to the West area of Fig.8 where relevance based on NIp is relatively low. Similarly , 67
percent of the prefectures in the quadrant D belongs to the North area of Fig.10 where relevancebased on NIm is relatively high. While, there is no prefecture in the East-South area in Fig.8.

17

NIm
46

2

18

2.5

42

D

2

32

1.5
1

43

0.5
33

-2

3
17

-1

0
-0.5

0

1

2

NIp

-1
-1.5
-2

Fig.8 Combination of two relevance indices in quadrant D

3.4.4 Economic geographical consideration on relevancies of prefectures
Considering the results observed in the previous analyses from the view point of economic geography,
the relevancies of the city systems of prefectures are summarized into the following four groups.
1)The structure of the city systems in the prefectures that play central roles in social andeconomic activities tends to be concentrative. And the city systems have high relevancies other city
systems through the passenger flow amounts, NIf, and the locations of the branch factories ofmanufacturing companies, NIp. While they have low relevancy through the locations of thebusiness/sales offices of manufacturing companies. Considering large passenger flow amounts due tohuge economic activities, it is inferred that they have high NIf and low NIm.
Prefecture that has an intensive city system and the three relevancy indicators are high is only
Toyama prefecture.
2) The prefectures located in the vicinity of the regions with large economic scale have large
economic activity. Thus, their city system are concentrative structure. These prefectures haverelatively high coopetition with the regions carrying out large social and economic activities. While,
they have relatively low connectivity with regions in rural area. Thus, the relevancies of the city
systems through the passenger flow amounts and the locations of the business/sales offices ofmanufacturing companies are low. On the other hand, the extent to which they have the relevancy
through the branch factories may depend on their industrial composition.
There is almost no prefecture that has an intensive city system and the high relevancy indicator
18

based on business/sales offices.
3) The city systems of the prefectures that depart from the economically active regions tend to beleveled. Some of these prefectures tend to have low relevance in passenger flow amount. The cause ofthis tendency may be considered as follows: since they have the heavy chemical industry in theirindustrial composition, they do not need to large passenger flow amounts. And It is considered thatthese prefectures may substitute for the passenger flow amounts with the locations of thebusiness/sales offices in manufacturing industry: The manufactured goods of industries in these
prefectures may need to secure a wide range of sales destinations, thus the relevancy through NIm
becomes high. The extent to which they have the relevancy through the branch factories may dependon their industrial composition. It is noteworthy that as shown by Kochi(39) prefecture, when aprefecture has a small economic scale and its location is departed from economically active region,
the relevancies of the city system based on the passenger flow amounts is not so low, the relevancies
through branch factories and business/sales offices of manufacturing companies are small. It seems to
be rather isolated city system. In the prefecture entering this group, there are few prefectures that there
are not many prefectures that have high relevancy through NIp and low relevancy through NIm.
4) Like the prefectures of 3) above, the city systems in the prefectures that are departed from theeconomically representative regions tend to be leveled. But others of these prefectures tend to haverelatively high relevance in passenger flow amount. Furthermore, there is prefecture that has very highrelevancy. The extent to which they have the relevancy through the branch factories may depend on
their industrial composition.
There is almost no prefecture that has a leveled city system and the high relevancy indicator basedon the branch factories of manufacturing industries.
Meanwhile, considering the relevancies of Ishikawa prefecture may give an insight in planningcity system: the city system of Ishikawa prefecture that has low CSI, which means that the city system
is level and its economic activity is not concentrated in the largest city. And this prefecture has highrelevancy based on passenger flow amount, which may mean that the prefecture is opened to otherregional economies. And it has low relevancies through NIp and NIm, this may indicate that thisprefecture has established an industrial and economic foundation locally in its own region. Thisprefecture would provide a good model which some prefectures in rural area should refer for vitalizing
regional economy: In order to autonomously revitalize local economic activities, it is necessary todevelop a local production organization. On the other hand, to maintain the organization, it is necessary
to capture large external demand, for which cooperation with the outside is indispensable. In addition,in order to further maintain social soundness, a level urban system is desirable. Ishikawa Prefecture
seems to have the possibility of meeting these requirements.

19

4 Conclusions
Cities are places where people's consumption activities and production activities are specificallyrealized. The economic activities in a city are not carried out isolatedly, but in cooperation with manyother cities. For this reason, many of the economic roles and characteristics of individual cities are set
in the framework of a city system. This city system is usually formed in an administrative area having
a certain geographical range. Therefore, the regional economy and the city system are interdependent
each other, and the scale and characteristics of economic activities in a region are represented in the
structure of the city system. Furthermore, as economic activity in general expands wider, themovement of goods expands on a global scale. In response to this globalization, an economic
cooperation is deepened among the city systems in many countries.
This paper examines the relevancies between the city systems by using three kinds of connection
indices: These indices are obtained by analyzing the passenger flow amounts(NIf), the locations of the
branch factories(NIp), and the locations and business/sales offices(NIm) of the companies inmanufacturing industry in 47 prefectures. The analysis of this paper shows the following things.
Prefectures that play a central social and economic function in the country and regions have highrelevancies with other areas in the indicators of NIf and NIp. Prefectures adjacent to areas playing acentral role have low relevancies through NIf and NIm. Many prefectures located far from areas
playing a central role have low relevancy through NIf. And the prefectures away from area with large
economic activities that have high relevancy through NIm. And among these prefectures, there are few
prefectures have low relevancy through NIm and high relevancy through NIp. It is shown in thisconsideration that even in prefectures located far away from areas with large economic activities, there
is prefecture that shows the possibility of maintaining autonomous economic activities by establishingproduction organization in its area and through many human interactions with other areas .
Since the economic activities in each prefecture are revealed on the city system, the relevancies
among the city systems are examined by using prefectural materials in this analysis and the data of thecompanies in manufacturing industry. As shown in this paper, the relevancy between the city systems
changes greatly depending on the index. In order to clarify cooperation of the city system in moredetail. It is needed to conduct more refined analysis from more materials. The results derived in thisanalysis are expected to be a kind of a clue for the future researches.

References
Beckmann, M.J., and McPherson, J.C. (1970) “City size distribution in a central place Hierarchy: An
alternative approach,” Journal of Regional Science, 10, 1. pp.25-33.
Capello, R. (2004) “Beyond optimal city size: Theory and evidence reconsidered, “Capello, R and R.
Nijkamp ed, Urban Dynamics and Growth, Amsterdam, Elsevier.
Christaller, W. (1933) Die Zentralen Orte in Süddeutschland, G.Fisher, Jena.
20

Hoover, E.M. (1970) “Transport Cost and the Spacing of Central Places,” Papers of Regional Science
Association, 25, pp.255-274.
Ishikawa, T. (2016) Dynamic locational phases of economic activity in the globalized world, Singapore,
Springer,
Toyo Keizai Shinposha, (2017) Kaisha-Shikiho（Data book）Tokyo.
Toyo Keizai Shinposha, (2016) Chiiki Keizai Soran（Data book）Tokyo.
Lösch, A. (1942) Die räumliche Ordnung der Wirtschaft, Jena, G. Fischer.
Parr, J.B. (1988) “Income, Trade and the Balance of Payments within an Urban
System,” Journal of Regional Science, 28, pp.1-14.
Sheppard, E. (1982) “City size distributions and spatial economic change,”
International Regional Science Review, 7, 2, pp.127-151.
Tinbergen, J. (1968) “The hierarchy model of the size distribution of centres,”
Papers in Regional Science Association, 20. pp.65-68.
Von Wouter et al (2005) Exploratory Social Network Analysis with Pajek, Cambridge, Cambridge
University Press.

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