Regional economic integration via detection of circular flow in international
value-added network

Sotaro Sada*,Yuichi Ikeda‡

Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto
University, Kyoto, Japan

*<EMAIL_ADDRESS>
‡<EMAIL_ADDRESS>
## Abstract

Global value chains (GVCs) are formed through value-added trade, and some
regions promote economic integration by concluding regional trade agreements
to promote these chains. However, there is no way to quantitatively assess the
scope and extent of economic integration involving various sectors in multiple
countries. In this study, we used the World Input–Output Database to create a
cross-border sector-wise trade in value-added network (international value-
added network (IVAN)) covering the period of 2000–2014 and evaluated them
using network science methods. By applying Infomap to the IVAN, we confirmed
for the first time the existence of two regional communities: Europe and the
Pacific Rim. Helmholtz–Hodge decomposition was used to decompose the value
flows within the region into potential and circular flows, and the annual
evolution of the potential and circular relationships between countries and
sectors was clarified. The circular flow component of the decomposition was
used to define an economic integration index, and findings confirmed that the
degree of economic integration in Europe declined sharply after the economic
crisis in 2009 to a level lower than that in the Pacific Rim. The European
economic integration index recovered in 2011 but again fell below that of the
Pacific Rim in 2013. Moreover, sectoral analysis showed that the economic
integration index captured the effect of Russian mineral resources, free
movement of labor in Europe, and international division of labor in the
Pacific Rim, especially in GVCs for the manufacture of motor vehicles and
high-tech products.

## Introduction

It is difficult to grow a country’s economy without establishing economic
relations with other countries. Every year, the amount of international trade
increases along with the world’s GDP. Free trade agreements (FTAs) and
regional trade agreements (RTAs) have been created to support this trend, and
countries are working to stabilize trade.

How, then, do countries become interdependent through trade? Classically,
Ricard advocated comparative advantage, which stated that countries
specializing in different industries are supposed to trade by taking advantage
of their respective strengths. However, in recent years, trade in intermediate
goods, which did not exist at that time, has begun and flourished. In other
words, there are forms of trade specializing in different industries and GVCs
in the same industry to produce complex and sophisticated products. In
addition, distance (as represented by the gravity model) and economic
integration (such as that promoted by the EU and NAFTA) facilitate
international trade.

Many studies have been conducted on measuring international production
structures. In the 21st century, measurement of GVCs became a widely discussed
topic after Hummels et al. [1] proposed the vertical specialization index.
Moreover, the VAX and FVAiX indices were proposed by Johnson and Noguera [2]
and Amador et al. [3], respectively. Koopman et al. [4] decomposed and
classified the trade prices into nine terms and clarified double-counted
terms.

The abovementioned progress has led to the development of international
input–output (IO) tables. After the World Input–Output Database (WIOD) was
publicized by Dietzenbacher et al. [5] and Timmer et al. [6] [7], Cerina et
al. [8] and Zhu et al. [9] analyzed the data for measuring GVCs network
analysis methods. Los et al. [10] showed that GVCs have been fragmenting more
rapidly than regionally in 1995–2011. According to Johnson and Noguera [11],
over a period of 40 years, the ratio of value-added to gross exports in non-
manufacturing sectors rose, while that in manufacturing sectors fell by 20
percentage points; their study showed that RTAs led to such decline.

Due to international relationship problems in the economy, researchers in
international organizations have been analyzing GVCs. Recently comprehensive
summary reports of GVC research have been published by the World Bank [12]
[13]. According to these reports, GVC research aims to address
misunderstanding of trade data and give international trade opportunities and
export diversity to developing countries for economic growth [14]. As shown by
Degain et al., GVCs had been expanding until the global financial crisis, but
it stopped growing in 2011 when it recovered from a decline in equipment. The
GVC expansion seen before the financial crisis has been interpreted as China’s
accession to the WTO and participation in GVCs [14]. These GVC research
developments were described in detail by Amador and Cabral [15] and Inomata
[16]. However, economics studies mainly focus on the relationship between
nations. There are limited works showing the complicated relationship between
industries in different countries.

By contrast, there are many studies on international trade in network science
because of recent developments in analytical methods and data availability.
Initially, the scale-free characteristics of international trade networks were
clarified [17][18][19]; then, the virtual nodes in these networks were
examined using centrality indices and other measures, and changes over time
were analyzed [20][21][22].

Ikeda et al. [23] [24] studied the international trade network of the WIOD
using community analysis of modularity maximization, which combines the
synchronization aspect of the G7 production network [25] [26]; then, they
found stable sectoral communities that had emerged in 1995–2011.

From an institutional point of view, a study examining interregional
agreements and geographic factors in international trade change found no
evidence that the WTO has contributed to the increase in international trade
and indicated that geographic factors are more significant than interregional
agreements [27]. By contrast, other studies show that trade policies
contribute to shaping trade networks [28], and the impact of distance by trade
is decreasing in industrial sectors [29].

However, there is no way to quantitatively assess the scope and extent of
economic integration involving various sectors in multiple countries. It is
difficult to quantitatively evaluate such economic phenomena, where multiple
countries and sectors are intertwined, and the trade balance between two
countries is still used as a basis for foreign economic policy. In this study,
we analyze the economic linkages through trade that have been made in recent
years using international IO tables and network science methods and clarify
how the world economy is being integrated from the perspective of value-added
trade.

In this context, this study offers the following essential contributions.
First, rather than using trade figures, which can mislead international
economic relations, we used the value-added calculations used in an IO
analysis to construct a sector-wise network. Next, from the value-added
linkage, we confirmed the regional characteristics of Europe and the Pacific
Rim. Findings showed that the behavior of this value-added relationship is
highly different from that of the sectoral community in the international
trade network shown in previous studies. The dense economic relationships
within these regions were decomposed into potential and circular
relationships, and the countries and sectors that contribute to the strong
regional ties were identified. Finally, we propose an economic integration
index that is based on the circular flow component, and the results showed
that economic integration was higher in the Pacific Rim than in Europe in
2010, 2013, and 2014.

The remainder of this paper is organized into three parts. The next section
describes the IO table and the computational method used in this work to
create the network and the community analysis, explains the decomposition of
the potential and circular flow components, and presents the proposed method
for measuring economic integration. Then, the characteristics and structure of
the network, the potential and circular relationships, and the results of the
integration index are presented, and the international economic linkages are
examined on the basis of these results. Finally, we conclude this study.

## Data and methods

This section consists of four subsections. First, we describe the WIOD and the
computational methods used to build the cross-border, sector-wise trade in
value-adde network (IVAN). Second, we briefly describe Infomap, a community
analysis algorithm, which was used to determine the extent to which economic
integration is occurring. Third, we explain the use of Helmholtz–Hodge
decomposition to extract the potential and circular nature of IVANs. Finally,
the economic integration index is defined.

### Data

We used the WIOD released in 2016, which includes 43 countries and classifies
the rest of the world (RoW) into 56 sectors. These countries and sectors are
listed in S1 Table. and S2 Table: List of sectors.. The country codes are the
same as those of the WIOD, but we simplified the sectoral codes. The WIOD has
IO tables for 2000–2014. Table 1 shows a simplified example of the table. The
IO table was developed by Leontief [30] and is now used globally to estimate
economic and environmental conditions. In this paper, we used the WIOD without
RoW because we aim to analyze the relationships of specific countries.

Table 1: World input–output table with two sectors in three countries.

| Intermediate demand | Final demand |
---|---|---|---
| Country A | Country B | Country C | Total output
| Sector 1 | Sector 2 | Sector 1 | Sector 2 | Sector 1 | Sector 2 | Country A | Country B | Country C |
Country A | Sector 1 | $Z_{1,1}$ | $Z_{1,2}$ | $Z_{1,3}$ | $Z_{1,4}$ | $Z_{1,5}$ | $Z_{1,6}$ | $FD_{1,1}$ | $FD_{1,2}$ | $FD_{1,3}$ | $T_{1}$
Sector 2 | $Z_{2,1}$ | $Z_{2,2}$ | $Z_{2,3}$ | $Z_{2,4}$ | $Z_{2,5}$ | $Z_{2,6}$ | $FD_{2,1}$ | $FD_{2,2}$ | $FD_{2,3}$ | $T_{2}$
Country B | Sector 1 | $Z_{3,1}$ | $Z_{3,2}$ | $Z_{3,3}$ | $Z_{3,4}$ | $Z_{3,5}$ | $Z_{3,6}$ | $FD_{3,1}$ | $FD_{3,2}$ | $FD_{3,3}$ | $T_{3}$
Sector 2 | $Z_{4,1}$ | $Z_{4,2}$ | $Z_{4,3}$ | $Z_{4,4}$ | $Z_{4,5}$ | $Z_{4,6}$ | $FD_{4,1}$ | $FD_{4,2}$ | $FD_{4,3}$ | $T_{4}$
Country C | Sector 1 | $Z_{5,1}$ | $Z_{5,2}$ | $Z_{5,3}$ | $Z_{5,4}$ | $Z_{5,5}$ | $Z_{5,6}$ | $FD_{5,1}$ | $FD_{5,2}$ | $FD_{5,3}$ | $T_{5}$
Sector 2 | $Z_{6,1}$ | $Z_{6,2}$ | $Z_{6,3}$ | $Z_{6,4}$ | $Z_{6,5}$ | $Z_{6,6}$ | $FD_{6,1}$ | $FD_{6,2}$ | $FD_{6,3}$ | $T_{6}$
Value-added | $VA_{1}$ | $VA_{2}$ | $VA_{3}$ | $VA_{4}$ | $VA_{5}$ | $VA_{6}$ |  |  |  |
Total output | $T_{1}$ | $T_{2}$ | $T_{3}$ | $T_{4}$ | $T_{5}$ | $T_{6}$ |  |  |  |

### Calculation for adjacency matrix of IVAN

Let $n_{c}$ be the number of countries and $n_{s}$ be the number of sectors in
the IO table. Then, we define the $n_{c}n_{s}\times n_{c}n_{s}$ intermediate
matrix $\mathbf{Z}$, $n_{c}n_{s}\times n_{c}$ final demand matrix
$\mathbf{FD}$, $1\times n_{c}n_{s}$ value-added vector $\mathbf{VA}$, and
$1\times n_{c}n_{s}$ total output matrix $\mathbf{T}$. With use of the value-
added vector $\mathbf{VA}$ and total output vector $\mathbf{T}$, the value-
added coefficient vector $\mathbf{V}$ is calculated as
$\mathbf{VA}/(\mathbf{T})^{\top}$. Therefore, an induced value-added vector
$\hat{\mathbf{V}}\mathbf{L}\mathbf{F}$ is made by a vector
$\mathbf{L}\mathbf{F}$ left-hand multiplied by the $n_{c}n_{s}\times
n_{c}n_{s}$ diagonal matrix $\hat{\mathbf{V}}$, where the diagonal components
are the vector $\mathbf{V}$.

Then, the adjacency matrix of the global value-added network (GVAN)
$\mathbf{G}$ is calculated as $\hat{\mathbf{V}}\mathbf{L}\hat{\mathbf{F}}$,
where $\hat{\mathbf{F}}$ is a diagonal matrix whose diagonal components are
the vector $\mathbf{F}$. The IVAN’s adjacency matrix $\mathbf{Y}$ was created
by eliminating components of 43 on-diagonal $56\times 56$ blocks as zero from
$\mathbf{G}$. This matrix represents the sum of all the ripple effects of
value-added induced by the final demand in foreign sectors. The GVAN and IVAN
nodes comprise 56 sectors in 43 countries. S1 Table. and S2 Table: List of
sectors. list these countries and sectors.

In summary, IVANs are directed and weighted networks constructed by the
adjacency matrix $Y$, which does not have domestic links. By contrast, GVANs
have domestic and international links.

### Community detection

To know how each network develop a community structure, we apply community
analysis to IVANs. Some community analysis methods have been developed, and
their features were summarized by Fortunato and Hric [33] and Barabási [34].
We used Infomap, which is an application of random walk and Huffman coding
[35] to analyze the communities in the studied network [36]. Let a random
walker run in the network where this analysis will be applied; the random
walker transitions with a probability dependent on the path weights (plus a
constant transposition probability) [37]. The map equation establishes
communities and renames the node in which the random walk track’s code length
is minimized. In comparison, the well-known method of modularity maximization
clusters a network by counting nodes’ link weights, inflows, and outflows,
whereas the map equation method clusters a network by the remaining time of
the random walker in the nodes; this difference leads to variations in results
[36] [32].

In the Infomap method, the optimization problem for community segmentation in
a network is replaced with the minimization problem of the code length of a
segmented network. Consider the segmentation of a network composed of $n$
nodes into $m$ communities with a community partition $\mathsf{M}$. Let the
mean code length of segmented communities (index code length) be
$H(\mathcal{Q})$ and the mean code length of nodes within a community $i$ be
$H(\mathcal{P}^{i})$; then, with use of Shannon’s source coding theorem [38],
the average description length of a single step of the random walk $L(M)$ is
calculated as follows:

$L(\mathsf{M})=q_{\curvearrowright}H(\mathcal{Q})+\sum_{i=1}^{m}p_{\circlearrowright}^{i}H(\mathcal{P}^{i}),$
(1)

where $q_{\curvearrowright}$ is the probability of the random walker moving to
another community and $p_{\circlearrowright}^{i}$ is the probability of the
random walker moveing within a community $i=1,2,\ldots,m$ plus the exit
probability from $i$. Each of the probabilities is defined as
$q_{\curvearrowright}=\sum_{i=1}^{m}q_{i\curvearrowright}$ and
$p_{\circlearrowright}^{i}=\sum_{\alpha\in
i}p_{\alpha}+q_{i\curvearrowright}$, where $p_{\alpha}$ is the probability of
visiting node $\alpha=1,2,\ldots,n$ and $q_{i\curvearrowright}$ is the exit
probability from community $i$. Eq (1) is called the map equation [32].

### Structural characteristics of networks

Certain indices reveal network characteristics. We used eleven indices: (1)
density, reciprocity, diameter, average path length, average betweenness,
assortativity, average in-degree, and average out-degree are calculated as
unweighted and directed networks; (2) in-strength and out-strength are for
weighted and directed ones; (3) the clustering coefficient is calculated as
unweighted and undirected [34].

The density of a network is the proportion of the number of links to the
number of maximum possible links in the network. Thus, it is calculated as
$l/n(n-1)$, where $n$ and $l$ are the numbers of nodes and links in the
network, respectively.

The reciprocity of a network is the proportion of the reciprocal links to the
total number of links in the network. It is calculated as $l_{m}/l$, where
$l_{m}$ is the number of reciprocal links (two directed links between two
nodes in the network).

The clustering coefficient indicates how each node is connected to its
neighbors. The clustering coefficient $c_{i}$ of a node $i$ is calculated as
$c_{i}=l_{i}/k_{i}(k_{i}-1)$, where $l_{i}$ ($k_{i}$) is the number of links
(neighbors) of node $i$. Thus, the clustering coefficient of a network is
$\sum c_{i}/n$.

The diameter of a network is the maximum number of shortest paths for all
pairs of nodes in the network.

The average path length of a network is the mean of the shortest path length
in the network: $\sum_{i,j;i\neq j}d_{ij}/n(n-1)$, where $d_{ij}$ is the
shortest path length between nodes $i$ and $j$.

The betweenness is calculated by the number of the shortest paths through a
node. The betweenness $b_{i}$ of node $i$ is $\sum_{j\neq k\neq
i}s_{jk}(i)/s_{jk}$, where $s_{jk}$ is the number of the shortest paths
between nodes $j$ and $k$, and $s_{jk}(i)$ is the number of the shortest paths
through node $i$. Therefore, the average betweenness of a network is the mean
of $b_{i}$.

The degree of a node means the sum of the number of links in the node. There
are two kinds of degrees in a directed network, namely, in-degree and out-
degree, which are the sums of the links to the node from the other nodes
(inflow) and links from the node to other nodes (outflow), respectively. Thus,
the in-degree and out-degree are represented as: $\sum_{j}l_{j,i}$ and
$\sum_{j}l_{i,j}$, respectively, where $l_{i,j}$ is a link (flow) from node
$i$ to node $j$.

The assortativity of a network scores the similarity of the connections in the
network as -1 to 1, which is calculated by
$(\sum_{jk}jke_{jk}-\mu)/\sigma^{2}$, where $e_{jk}$ is the probability of the
two nodes of degrees $j$ and $k$ are at the end of a randomly chosen link, and
$\mu$ and $\sigma$ are the mean and standard deviation, respectively, of the
excess degree distribution. Assortativity that is close to -1 (1) indicates
that high-degree nodes in a network are connected to low-degree nodes (high-
degree nodes).

The strength of a node is the total weight of the links in the node. There are
two kinds of strength, in a directed network, namely, in-strength and out-
strength, which are the summed weights of the inflow and outflow,
respectively. Thus, the in-strength and out-strength are represented as:
$\sum_{j}l^{w}_{j,i}$ and $\sum_{j}l^{w}_{i,j}$, respectively, where
$l^{w}_{i,j}$ is the flow amount from node $i$ to node $j$.

### Decomposition to potential and circular flows

Firstly, we define flows as directed and weighted links, and the flow of IVANs
as value flow. We used Helmholtz–Hodge decomposition [39] to extract potential
and circular relationships from IVANs. This method was also used by Kichikawa
et al. [40] to clarify the potential relationships in corporate transaction
networks. With Helmholtz–Hodge decomposition, the flow $F_{ij}$ from node $i$
to node $j$ can be separated into the circular flow $F_{ij}^{(c)}$ and
potential flow $F_{ij}^{(p)}$: $F_{ij}=F_{ij}^{(c)}+F_{ij}^{(g)}$. Here the
potential flow $F^{(p)}_{ij}$ is given by
$F^{(p)}_{ij}=w_{ij}(\phi_{i}-\phi_{j})$, where $\phi_{i}$ is the
Helmholtz–Hodge potential and $w_{ij}$ is a positive weight for the link
between node $i$ and node $j$. The circular flow satisfies
$\sum_{j}F^{(c)}_{ij}=0$, in which the inflows and outflows are balanced in
each node. $F_{ij}^{(p)}$ represents the difference in potentials between the
nodes, whereas $F_{ij}^{(c)}$ represents the number of feedback loops among
the nodes.

An IVAN captures the value-added chain of various international sectors to
their respective final goods. The potential of a sector is the difference
between the amount of value adde by the sector for final foreign production
and the amount of value added by the foreign sector for the sector’s final
production. In other words, if the value-added potential is positive, the
sector contributes more to the production of the final goods of the foreign
sector, and if it is negative, the sector is contributed more to the own
production of the final goods by foreign sectors. This can indicate the degree
of asymmetric dependence or co-dependence. Moreover, the circular flow
component indicates the amount of contribution to (from) the foreign sector,
that is, the degree of interdependence.

### Economic integration index

When several economies proceed with economic integration by some factors such
as the establishment of FTAs or RTAs, the value added in a country becomes
increasingly induced by other countries, and vice versa. In other words,
higher economic integration makes a larger feedback loop within an IVAN. On
the basis of this assumption, we define the economic integration index $E$ as
the aggregate amount of circular flow divided by the total flow of the GVAN in
a specific community.

$E=\frac{\sum_{i>j}Y_{ij}^{(c)}}{\sum G_{ij}}$ (2)

The range of application of this index covers communities detected by Infomap,
which also detects communities using flow. The detected communities are
interpreted as the circulation observed when random walkers rotate in the
community. The degree of circulation is quantified and divided by the economic
scale of the community; then, the economic integration is measured as the
amount of value-added circulation per economic scale.

The index defined here indicates how much of the domestic and international
value-added chain toward final demand can be extracted as international
interdependence. The higher the value of the index, the greater the value-
added induced in the community across national borders (economic activities
performed by sectors in other countries), and economic integration in this
study is measured by this value.

This economic integration index can decompose into sectoral indices
arbitrarily. For sector $k$, the sectoral economic integration index is

$E_{k}=\frac{\sum_{i>j;i,j\in S_{k}}Y_{ij}^{(c)}}{\sum_{i,j\in S_{k}}G_{ij}},$
(3)

where $S_{k}$ is a set of nodes in sector $k$.

In summary, the economic integration index is the circular magnitude of the
cross-border value-added contribution of economic activities in a country
(other countries) toward the final production of sectors in other countries
(home country), compared with the circular magnitude of the value-added
contribution of economic activities in the community, including circulation
within a country.

## Results

This section is composed of three subsections. The first subsection shows the
community structure of the IVANs, the threshold set for community detection,
and the resulting 15-year change in regional communities. The second
subsection shows the basic characteristics of the original IVAN, the cut IVAN,
and the IVAN of the regional communities in selected years. The third
subsection confirms the value-added potential and circular relationships
revealed by Helmholtz–Hodge decomposition for countries and sectors in Europe
and the Pacific Rim. The last subsection shows the evolution of economic
integration in the regional communities and the results of decomposing the
economic integration indicators into key sectoral components.

### Communities of IVANs

Direct application of Infomap to the IVANs reveals one large community for 15
years. This result differs from the community of international trade network
shown in a previous study. Next, thresholds are set to exclude the branches
and leaves of the IVANs to see any concealed community structure. In the range
of 6,500–11,000 remaining links, several large communities appear (Fig 1).
Here, the thresholds are set by the number of the most extensive links to be
retained, as the threshold value set by USD is inappropriate for the weight of
the IVAN links, which fluctuates due to the economic growth and economic
crisis that occurred in those 15 years. In Fig 1, each cell colored on the
number of communities with more than 240 nodes which is 10% of the total nodes
in the IVANs. The remaining number of links in 2014 is almost half of that in
2004–2009.

Fig 1: Heat map of the number of large communities in the IVANs cut by each
threshold, in 2000–2014. This research uses the thresholds represented as a
red cell in each year. Colors means the number of communities.

By using the abovementioned threshold values, we can detect the communities
from the IVANs as shown in Fig 2 which shows four years’ heat maps and
represents each cell as a node of the IVANs. In the maps, the separated
communities are indicated by different colors; the gray cells are the nodes
that were not considered communities. The figure shows orange horizontal
stripes, which include most of the sectors in countries such as Australia,
Brazil, and Canada. The green nodes include the sectors A01: agriculture, C29:
manufacture of motor vehicles, and C30: manufacture of other transport
equipment of mainly European countries. The gray area includes many other
sectors in Europe, especially in small countries.

Fig 2: Community heat maps in 2000, 2004, 2009, and 2014. Each cell is a node
of IVAN, the gray nodes are not a communities, while the other colors indicate
community. The green and orange cells are nodes of the European and Pacific
Rim communities, respectively. The regional classification is in S1 Table..

The results of community detection 15 years are shown in Fig 3 as a Sankey
diagram, where orange represents the Pacific Rim sectors, and the green
represents the European sectors (nodes) (the details of the classification are
in S1 Table.), and we can see that these two regions are detected as separate
communities throughout the 15 years.

Fig 3: Sankey diagram of communities in 2000–2014. Communities are ordered by
size, from the largest to the smallest, each year. Green and orange represent
nodes of Europe and the Pacific Rim, respectively. Their classification of
them is in S1 Table.. The two bottom communities are used to denote regional
communities, but there have been other small European communities over the
years.

### Observed structural characteristics

Table 2 shows the structural features for 2000, 2008, and 2014. The densities
and cluster coefficients show that the IVANs are dense, and the reciprocity
shows that more than 97% of the links are mutual. The density of the IVANs
that are cut at the threshold in Fig. 1 is reduced by about 82%. In terms of
reciprocities, the cut IVANs are about 20% of the remaining links that are
cut. This indicates that the IVAN have many asymmetric mutualities with large
values in only one direction. In the two local communities, the cluster
coefficients and reciprocities are at the same level as those of the IVANs,
although the densities are about 10% higher than those of the entire IVANs.

Table 2: Structural characteristics of IVANs, IVANs cut with the threshold,
IVANs in the regional communities: Europe and the Pacific Rim.

| 2000 | 2008 | 2014
---|---|---|---
| IVAN | Cut IVAN | Europe | Pacific Rim | IVAN | Cut IVAN | Europe | Pacific Rim | IVAN | Cut IVAN | Europe | Pacific Rim
Density | 0.831 | 0.0174 | 0.942 | 0.921 | 0.841 | 0.0184 | 0.955 | 0.925 | 0.831 | 0.0112 | 0.945 | 0.929
Reciprocity | 0.972 | 0.231 | 0.987 | 0.976 | 0.982 | 0.192 | 0.990 | 0.987 | 0.974 | 0.169 | 0.993 | 0.975
Clustering coefficient | 0.976 | 0.321 | 0.953 | 0.941 | 0.976 | 0.319 | 0.963 | 0.934 | 0.976 | 0.278 | 0.950 | 0.950
Diameter | 2 | 5 | 2 | 2 | 2 | 4 | 2 | 2 | 2 | 6 | 2 | 2
Average path length | 1.023 | 2.474 | 1.046 | 1.056 | 1.023 | 2.55 | 1.035 | 1.063 | 1.023 | 2.656 | 1.048 | 1.048
Average betweenness* | 51.70 | 2644 | 24.62 | 37.14 | 51.72 | 3053 | 28.99 | 37.37 | 51.64 | 2835 | 14.32 | 35.82
Assortativity | -0.0167 | -0.436 | -0.0394 | -0.0304 | -0.0179 | -0.427 | -0.0294 | -0.0305 | -0.0170 | -0.424 | -0.0505 | -0.0304
Average in-degree* | 2196 | 71.68 | 516.4 | 622 | 2198 | 71 | 788 | 556.8 | 2193 | 52.59 | 281.7 | 715.3
Average out-degree* | 2143 | 68.71 | 509.7 | 610.7 | 2164 | 65.5 | 780.3 | 553 | 2147 | 45.61 | 279.8 | 703

*These averages were calculated for nonzero values.

Each IVAN has a diameter of 2, which means that any sector in any country can
be connected to all sectors through one sector in another country. The minimum
diameter is 2 because links to sectors in the same country are not included,
but since the average path length is close to 1, most sectors are directly
connected. In the cut IVANs, the diameter is about 5, and the average
betweenness is more than 50 times larger than that of the original IVANs
because the diameter and average path length are long, and a particular node
mediates many shortest paths. In the regional communities, the average path
length is a slightly longer, and the betweenness is roughly half of the
original IVANs.

The number of nodes in the IVANs is 2,408, but the average in-degree and out-
degree value is over 2,100. Since most of the sectors are connected, the
assortativity is close to zero. In the cut IVANs, the degrees and
assortativity are around 70 and -0.43, respectively, indicating that sectors
with degree differences are connected by high values flows. In the regional
communities, the degree varies according to the size of the detected regional
community, and the assortativity is negative, close to zero.

Fig 4 shows a wide strength distribution of the IVAN’s. The distribution of
Fig 4 partly fits a log-normal distribution, especially in the right tail. The
probability density function of a log-normal distribution $p(x)$ for $x>0$ is:

$p(x)=\frac{1}{\sqrt{2\pi}\sigma x}\exp\biggl{[}-\frac{(\log
x-\mu)^{2}}{2\sigma^{2}}\biggr{]},$ (4)

where $\mu$ and $\sigma$ are the mean and standard deviation of the logarithm,
respectively. As seen in Fig 4, the mean and standard deviation of the
logarithm of strength distribution in 2014 are $\mu=5.959$ and $\sigma=2.129$
in in-strength, and $\mu=6.146$ and $\sigma=2.001$ in out-strength,
respectively.

Fig 4: Cumulative probability of strength of IVAN in 2000, 2008, and 2014. The
black lines are plots of the cumulative density function of the log-normal
distribution whose $\mu$ and $\sigma$ are equal to the average and the
standard deviation, respectively, of the logarithm of strength distribution in
2014. Their right tails are almost fitted, but the left tails are not,
especially at the bottom.

### Potential and circular relationships in two regional communities

Helmholtz–Hodge decomposition was applied to the two regional communities
detected by Infomap. The size of the circular flow component and the value of
the IVAN link (value flow) are well correlated in the range where the value
flow is greater than 100 million USD, as shown in Fig 5. In the economic
integration index, the amount of circular flow is divided by the GVAN weights;
thus, the economic scale does not appear directly.

Fig 5: Scatter plot of correlation between circular flow and value flow in
2000. The larger circular flows are in proportion to the original value flows,
but the lower flows are disarranged.

The potential and circular relationships in Europe and the Pacific Rim can be
analyzed from the international and intersectoral perspectives by aggregating
nodes into countries and sectors.

#### Europe

Tables 2–7 show the breakdown of the potential and circular relationships in
Europe, which is obtained from the Helmholtz–Hodge decomposition. In terms of
countries, the value potential is mainly high in Russia, Norway, and Germany
and low in France, Spain, and Italy (Table 3). From 2003 to 2012, Russia and
Norway mainly have the first and second highest potential, respectively. In
2001, 2002, and 2010, with changes in the ranking of the communities in Fig 3,
Germany shows the highest potential. In 2000 and 2001, 2010, and since 2013,
when the European community was relatively small (Fig 3), Russia had not been
in Table 3. In addition, Belgium, Switzerland, and the Netherlands repeatedly
appear in Table 3. Non-European countries, such as the United States, are
ranked fourth from 2002 to 2005, while China is fourth in 2009 and 2010.
France is ranked the lowest-potential country except in 2002 and 2003, when
Spain is ranked first, followed by Italy (Table 4). Portugal and Turkey are
also ranked in half of the years. Tables 3 and 4 show that Germany is ranked
as both a high-potential and low-potential country.

Table 3: Five highest-potential countries in Europe.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | NLD | DEU | DEU | RUS | RUS | RUS | RUS | RUS | RUS | RUS | DEU | RUS | RUS | POL | DEU
2 | DEU | BEL | RUS | NOR | NOR | NOR | NOR | NOR | NOR | NOR | GBR | NOR | NOR | ITA | RUS
3 | CHE | CHE | NOR | DEU | DEU | DEU | DEU | DEU | NLD | DEU | BEL | NLD | NLD | CZE | NLD
4 | BEL | NLD | USA | USA | USA | USA | NLD | NLD | CHE | CHN | CHN | IRL | DNK | AUT | GBR
5 | NOR | FIN | NLD | NLD | BEL | BEL | USA | BEL | AUT | BEL | AUT | CYP | USA | NLD | HUN

Table 4: Five lowest-potential countries in Europe.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | FRA | FRA | ESP | ESP | FRA | FRA | FRA | ESP | FRA | FRA | FRA | FRA | FRA | FRA | FRA
2 | ESP | ESP | ITA | FRA | ESP | ESP | ESP | FRA | ESP | ITA | ITA | DEU | DEU | BEL | CHE
3 | ITA | DNK | FRA | ITA | ITA | ITA | ITA | GBR | DEU | ESP | ESP | ITA | GBR | GBR | DNK
4 | PRT | PRT | POL | POL | HUN | TUR | TUR | TUR | TUR | GBR | LUX | GBR | TUR | RUS | ESP
5 | DNK | POL | PRT | HUN | POL | HUN | POL | ITA | POL | LUX | DNK | POL | POL | DEU | TUR

Russia is ranked first in the high-potential tables (Tables 3 and 5) except
for 2002, when sector B: mining and quarrying is ranked first. If the sector
B: mining and quarrying was not considered in Table 5 and Russia were not
included in Table 3. The other highest-potential sectors in Europe are M69:
legal, accounting, and consultancy activities in 2000 and 2010; C24:
manufacture of basic metals in 2001; C25: manufacture of fabricated metal
products, except machinery and equipment in 2013; and G46: wholesale trade
except that of motor vehicles and motorcycles in 2014. In addition, sectors N:
administrative and support service activities and C20: manufacture of
chemicals and chemical products are often ranked high. In terms of low
potential (Tables 4 and 6), sector F: construction is ranked first throughout
the 15 years, followed by sectors C28: manufacture of machinery and equipment,
C19: manufacture of coke and refined petroleum products, C29: manufacture of
motor vehicles, which occupy the second and subsequent positions; O84: public
administration and defense, and compulsory social security, which appears in
the third and subsequent positions; and L68: real estate activities, which
often appears in the fifth position.

Table 5: Five highest-potential sectors in Europe.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | M69 | C24 | B | B | B | B | B | B | B | B | M69 | B | B | C25 | G46
2 | C24 | N | N | N | N | N | N | C24 | C24 | M69 | G46 | G46 | G46 | C24 | C24
3 | N | M69 | M69 | M69 | M69 | C24 | C24 | N | G46 | N | N | N | N | C22 | C25
4 | C20 | C20 | C24 | C24 | C24 | M69 | M69 | G46 | M69 | G46 | C24 | C24 | M69 | G46 | C20
5 | K64 | C25 | C20 | C20 | C20 | G46 | G46 | M69 | H49 | C24 | C20 | H49 | C24 | C27 | C22

B: mining and quarrying; C20: manufacture of chemicals and chemical products;
C22: manufacture of rubber and plastic products; C24: manufacture of basic
metals; C25: manufacture of fabricated metal products except machinery and
equipment; C27: manufacture of electrical equipment; G46: wholesale trade
except trade of motor vehicles and motorcycles; H49: land transport and
transport via pipelines; K64: financial service activities except insurance
and pension funding; M69: legal and accounting activities; activities of head
offices, and management consultancy activities; N: administrative and support
service activities.

Table 6: Five lowest-potential sectors in Europe.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F
2 | C28 | C28 | C28 | C28 | C19 | C19 | C19 | C29 | C29 | C19 | C28 | C19 | C19 | C29 | C28
3 | C19 | O84 | O84 | O84 | C28 | C28 | C28 | C19 | C19 | C28 | O84 | C28 | C28 | C28 | O84
4 | O84 | C31 | C19 | C19 | O84 | O84 | O84 | C28 | C28 | O84 | G47 | D35 | D35 | O84 | G47
5 | C31 | L68 | L68 | L68 | L68 | R_S | R_S | O84 | O84 | L68 | C31 | O84 | O84 | R_S | C33

C19: manufacture of coke and refined petroleum products; C28: manufacture of
machinery and equipment n.e.c.; C29: manufacture of motor vehicles, and
trailers, and semi-trailers; C31: manufacture of furniture, and other
manufacturing; C33: repair and installation of machinery and equipment; D35:
electricity, gas, steam and air conditioning supply; F: construction; G47:
retail trade except that of motor vehicles and motorcycles; L68: real estate
activities; O84: public administration and defense, and compulsory social
security; R_S: other service activities.

According to the amount of circulation (Table 7), Germany is the top country
for the 15 years, followed by France, the United Kingdom, Italy, and Russia.
In terms of sectoral ranking (Table 8), sector F: construction is always
ranked first until 2010. In 2011 and 2012, sector B: mining and quarrying,
which often ranks second, is ranked first. In 2013, sector C29: manufacture of
motor vehicle is first. Russia is ranked second in the year that sector B:
mining and quarrying is ranked first. Throughout the whole years, F:
construction is first, followed by B: mining and quarrying, C28: manufacture
of machinery and equipment, C19: manufacture of coke and refined petroleum
products, and G46: wholesale trade except for that of motor vehicles and
motorcycles.

Table 7: Five-highest circulated countries in Europe.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU | DEU
2 | FRA | FRA | GBR | FRA | FRA | FRA | FRA | FRA | RUS | FRA | FRA | RUS | RUS | FRA | FRA
3 | NLD | ITA | FRA | ITA | GBR | GBR | GBR | ITA | FRA | RUS | ITA | NOR | GBR | ITA | ITA
4 | ITA | ESP | ITA | GBR | ITA | ITA | RUS | RUS | ITA | GBR | ESP | FRA | NOR | ESP | POL
5 | ESP | GBR | ESP | ESP | NLD | RUS | ITA | GBR | NOR | ITA | NLD | GBR | FRA | POL | AUT

Table 8: Five-highest circulated sectors in Europe.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | F | F | F | F | F | F | F | F | B | F | F | B | B | C29 | F
2 | C28 | C28 | B | B | B | B | B | B | F | B | C28 | F | F | F | C28
3 | G46 | G46 | N | N | C19 | C19 | C19 | C29 | C19 | C19 | G46 | C19 | C19 | C28 | G46
4 | K64 | C20 | G46 | G46 | N | G46 | G46 | C19 | C29 | G46 | M69 | G46 | D35 | C25 | C25
5 | C20 | C24 | C28 | C28 | G46 | C28 | C28 | G46 | G46 | D35 | K64 | D35 | G46 | C24 | C20

B: mining and quarrying; C19: manufacture of coke and refined petroleum
products; C20: manufacture of chemicals and chemical products; C24:
manufacture of basic metals; C25: manufacture of fabricated metal products,
except machinery and equipment; C28: manufacture of machinery and equipment
n.e.c.; C29: manufacture of motor vehicles, and trailers and semi-trailers;
D35: electricity, gas, steam and air conditioning supply; F: construction;
G46: wholesale trade except that of motor vehicles and motorcycles; K64:
financial service activities except insurance and pension funding; M69: legal
and accounting activities, activities of head offices, and management
consultancy activities; N: administrative and support service activities.

For both countries and sectors, those ranked higher or lower in terms of
potential are also greater in terms of circular strength, which is the
strength of the circular network decomposed from an IVAN. The relationship
between the circular strength and the Helmholtz–Hodge potential is shown in
Fig 6. The relationship is V-shaped; in other words, the larger the absolute
value of the potential, the higher the circular strength.

Fig 6: Scatter plot of correlation between circular strength and
Helmholtz–Hodge potential in Europe in 2000, 2008, and 2014. Each year shows a
V-shaped pattern, but the inclination is changed (sharpest in 2008 and
gentlest in 2014).

#### Pacific Rim

The characteristics of the potential and circular flows of the IVANs in the
Pacific Rim are shown in Tables 8–13. Japan, which has the maximum potential
in 2000 and 2002, has been out of the ranking since 2012; Canada shows the
maximum potential from 2003 to 2007, and Australia has been the highest-
potential country since then (Table 9). Indonesia, Taiwan, and India are also
among the five highest-potential countries. In terms of low potential, Mexico
is the top-ranked country until 2002, the United States from 2004 to 2006, and
China in 2003 and from 2007 to 2013. In addition, India, the United Kingdom,
and France appear in Table 10 numerous times.

Table 9: Five highest-potential countries in the Pacific Rim.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | JPN | CAN | JPN | CAN | CAN | CAN | CAN | CAN | AUS | AUS | AUS | AUS | AUS | AUS | AUS
2 | CAN | JPN | CAN | JPN | JPN | JPN | AUS | AUS | CAN | CAN | JPN | CAN | CAN | CAN | CAN
3 | AUS | AUS | AUS | AUS | AUS | AUS | JPN | JPN | IDN | JPN | CAN | IDN | IDN | TWN | TWN
4 | IDN | IDN | TWN | IDN | IDN | IDN | IDN | TWN | TWN | TWN | IDN | JPN | TWN | RUS | KOR
5 | TWN | TWN | IDN | TWN | KOR | TWN | TWN | IDN | BRA | IDN | TWN | TWN | BRA | IDN | DEU

Table 10: Five lowest-potential countries in the Pacific Rim.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | MEX | MEX | MEX | CHN | USA | USA | USA | CHN | CHN | CHN | CHN | CHN | CHN | CHN | USA
2 | CHN | CHN | USA | USA | CHN | CHN | CHN | USA | USA | MEX | MEX | IND | USA | USA | CHN
3 | USA | GBR | CHN | MEX | MEX | MEX | MEX | MEX | MEX | IND | GBR | MEX | IND | MEX | MEX
4 | GBR | IND | IND | IND | GBR | IRL | IRL | IND | KOR | GBR | IND | KOR | MEX | IDN | IND
5 | IND | USA | FRA | FRA | IND | IND | GBR | HUN | HUN | DEU | KOR | USA | FRA | GBR | GBR

In terms of sectoral potential (Tables 11 and 12), as in Europe, B: mining and
quarrying is the highest-potential sector, and F: construction is the lowest-
potential sector. The relationship is more stable than that in Europe and
remains unchanged over the 15 years. In addition, as shown in Table 11,
sectors B: mining and quarrying, C20: manufacture of chemicals and chemical
products, C24: manufacture of basic metals, G46: wholesale trade, K64:
financial service activities, and N: administrative and support service
activities are included in the high-potential sectors. Sectors F:
construction; O84: public administration and defense, and compulsory social
security; C29: manufacture of motor vehicles; C10: manufacture of food
products, beverages, and tobacco products; and Q: human health and social work
activities are among the lowest-potential sectors until 2009 except 2001.
Since 2010, Q: human health and social work activities have risen to higher
than third place.

Table 11: Five highest-potential sectors in the Pacific Rim.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B
2 | C20 | C20 | C20 | C20 | C20 | C24 | C24 | C24 | C24 | C24 | C20 | C24 | C24 | G46 | G46
3 | C24 | C24 | C24 | C24 | C24 | C20 | C20 | G46 | G46 | C20 | G46 | C20 | G46 | C24 | C24
4 | G46 | G46 | G46 | G46 | G46 | G46 | G46 | C20 | C20 | G46 | C24 | G46 | C20 | C20 | C20
5 | N | N | C25 | K64 | K64 | K64 | K64 | K64 | K64 | K64 | N | N | K64 | K64 | K64

B: mining and quarrying; C20: manufacture of chemicals and chemical products;
C24: manufacture of basic metals; C25: manufacture of fabricated metal
products except machinery and equipment; G46: wholesale trade except that of
motor vehicles and motorcycles; K64: financial service activities except
insurance and pension funding; N: administrative and support service
activities.

Table 12: Five lowest-potential sectors in the Pacific Rim.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F
2 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | Q | O84
3 | C29 | C29 | C29 | C29 | C29 | C29 | C29 | C29 | C29 | C29 | Q | Q | Q | O84 | Q
4 | C10 | Q | C10 | C10 | C10 | C10 | C10 | C10 | C10 | C10 | C29 | C29 | C29 | C29 | C29
5 | Q | C10 | Q | Q | Q | Q | Q | Q | Q | Q | C10 | C10 | C10 | C10 | C10

C10: manufacture of food products, beverages and tobacco products; C29:
manufacture of motor vehicles, and trailers and semi-trailers; F:
construction; O84: public administration and defense, and compulsory social
security; Q: human health and social work activities.

In terms of circulation (Tables 13 and 14), the United States is consistently
in the first place, followed by Japan, Canada, and China since 2007. Since
2005, Japan has been in the fourth place, followed by Mexico. By contrast, the
sector rankings in Table 14 are not as consistent as those of the countries.
In 2000 and 2007, C26: manufacture of computer, electronic, and optical
products is ranked first; in 2008 and 2011, B: mining and quarrying is ranked
first. These three sectors remain in the top three positions over the 15
years. They are followed by C29: manufacture of motor vehicles and O84: public
administration and defense, and compulsory social security until 2009, and by
O84: public administration and defense, and compulsory social security and Q:
human health and social work activities since 2010.

Table 13: Five highest-circulated countries in the Pacific Rim.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | USA | USA | USA | USA | USA | USA | USA | USA | USA | USA | USA | USA | USA | USA | USA
2 | JPN | CAN | CAN | CAN | CAN | CAN | CAN | CHN | CHN | CHN | CHN | CHN | CHN | CHN | CHN
3 | CAN | JPN | JPN | JPN | JPN | CHN | CHN | CAN | CAN | CAN | CAN | CAN | CAN | CAN | CAN
4 | MEX | MEX | MEX | CHN | CHN | JPN | JPN | JPN | JPN | JPN | JPN | JPN | JPN | JPN | JPN
5 | CHN | CHN | CHN | MEX | MEX | MEX | MEX | MEX | MEX | MEX | MEX | MEX | MEX | MEX | MEX

Table 14: Five highest-circulated sectors in the Pacific Rim.

Rank | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1 | C26 | F | F | F | F | F | F | C26 | B | F | F | B | B | F | F
2 | F | C26 | C26 | C26 | B | B | B | F | C26 | B | B | F | F | B | B
3 | B | B | B | B | C26 | C26 | C26 | B | F | C26 | C26 | C26 | C26 | C26 | C26
4 | C29 | O84 | C29 | O84 | O84 | C29 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84 | O84
5 | O84 | C29 | O84 | C29 | C29 | O84 | C29 | C29 | C29 | C29 | C29 | Q | Q | Q | Q

B: mining and quarrying; C26: manufacture of computer, electronic, and optical
products; C29: manufacture of motor vehicles, and trailers and semi-trailers;
F: construction; O84: public administration and defense, and compulsory social
security; Q: human health and social work activities.

As in Europe, the high- or low-potential countries and sectors in the Pacific
Rim are high in circular strength. The relationship between the circular
strength and the Helmholtz–Hodge potential is shown in Fig 7. The V-shaped
relationship between them is the same as that in Europe. However, there is a
difference in the tables 2–14. Sector C26: manufacture of computer,
electronic, and optical products does not appear in Tables 11 and 12, which
indicates a large value-added circulation in the midstream of the Pacific
Rim’s value flow, although all high-circular-strength sectors in Europe are
also in the value-added potential ranking.

Fig 7: Scatter plot of correlation between circular strength and Helmholtz-
Hodge potential in the Pacific Rim in 2000, 2008, and 2014. The years show the
similar inclinations of the V shape.

### Economic integration index

The results of applying the economic integration index to the two regional
communities are shown in Fig 8. The Pacific Rim shows a stable and upward
trend for economic integration, while Europe shows a higher but more unstable
integration level. In particular, there is a large decline in the level of
integration in 2009 and 2010, after the economic crisis, while the Pacific Rim
is slightly affected in 2009.

Fig 8: Economic integration estimation of the two regional communities in
2000–2014.

Figs 9, 10, and 11 show the sector-wise economic integration indices, focusing
on the sectors that show high circulation in Tables 8 and 14. As illustrated
in Fig 9, Europe exhibits a fivefold increase in 2007 and 2008 (just before
the economic crisis) in sector B: mining and quarrying and F: construction
(the top-ranking sectors in terms of potential and circular flows) compared
with 2000, then a sharp decline from 2009 to 2010 (below 2000 level). The low
values in 2010, 2013, and 2014 are partly due to a decline in F: construction,
but the circulation within B: mining and quarrying is almost zero. By
contrast, in the Pacific Rim, these values are tripled between 2007 and 2008;
they decline beginning 2011, but they remain above 2007 levels in 2014.

Fig 9: Sectoral economic integration index of mining and quarrying, and
construction. B: mining and quarrying, F: construction.

Fig 10 shows the sectoral economic integration indices of the manufacturing
sectors ranked in Tables 8 and 14. The figure illustrates that the increase in
the amount of circulation in the manufacturing sectors plays a major role in
Europe having the largest economic integration index in 2008. Sector C29:
manufacture of motor vehicles makes a significant contribution in 2007 and
2008. Sectors C24: manufacture of basic metals, C25: manufacture of fabricated
metal products, and C29: manufacture of motor vehicles exhibit the highest
values in 2008. The high value in 2008 can be seen from the fact that C24:
manufacture of basic metals, C25: manufacture of fabricated metal products,
and C29: manufacture of motor vehicles show the highest values throughout the
15 years. As for the manufacturing sectors, C19: manufacture of coke and
refined petroleum products disappears from the European community at a time
when the economic integration index for B: mining and quarrying is nearly
zero. On the contrary, in the Pacific Rim, the manufacturing sector steadily
increases its contribution to economic integration. In the years with large
values in economic integration index, C19: manufacture of coke and refined
petroleum products, C20: manufacture of chemicals and chemical products, and
C29: manufacture of motor vehicles are large in sectoral indices.

Fig 10: Sectoral economic integration index of manufacture. C19: manufacture
of coke and refined petroleum products; C20: manufacture of chemicals and
chemical products; C24: manufacture of basic metals, C25: manufacture of
fabricated metal products except machinery and equipment; C26: manufacture of
computer, electronic, and optical products; C28: manufacture of machinery and
equipment n.e.c.; C29: manufacture of motor vehicles, and trailers and semi-
trailers.

Finally, Fig 11 shows the other sectors that are ranked three or more times in
Tables 8 and 14. When Europe shows a high degree of economic integration, the
contributions of G46: wholesale trade, K64: financial service activities, and
N: administrative and support service activities are large. The contributions
of K64: financial service activities and N: administrative and support service
activities become so small after 2013, when the level of integration is low,
that they are barely visible. In the Pacific Rim, the contributions of G46:
wholesale trade; O84: public administration and defense, and compulsory social
security; and Q: human health and social work activities are large, although
they tend to peak and decline every three years except for 2009, when the
economic crisis occurred.

Fig 11: Sectoral economic integration index of other important sectors. G46:
wholesale trade except that of motor vehicles and motorcycles; K64: financial
service activities except insurance and pension funding; N: administrative and
support service activities; O84: public administration and defense, and
compulsory social security; Q: human health and social work activities.

## Discussion

In the international trade networks used by Ikeda et al.[24], the communities
are divided into industries; in original IVANs, the entire world is connected.
Two buried communities—Europe and the Pacific Rim—were identified in the
current paper by eliminating low flows with a threshold. However, since the
IVAN included only 43 countries (excludes RoW), a more extensive international
economic network, that is, one that includes other countries, may reveal more
than two regional communities can.

The variability between the threshold and the community detection results is
also important. In this study, we did not set the threshold as a specific
weight in order to see the change over the 15 studied years. This is because
the weights of IVAN links increase or decrease depending on economic growth or
crisis; thus, it was inappropriate to use the same value as the threshold
throughout the 15 years. In addition, as seen in Fig 1, the results of the
detected communities are unstable, even for close threshold values. The
threshold value did not separate the state of whether a single large community
or two communities appeared; rather, the trend of the distribution changed. In
this study, we used a resolution of every 500 links, but more detailed
research is needed on the relationship between the number of remaining links
and the number of detected communities. Thus, the threshold with the most
remaining links was used for this analysis. The impact of this approach on the
results is limited because the threshold was only applied for detecting
concealed communities; it was not adopted for calculating the economic
integration. With the threshold value we adopted, two communities with more
than 240 nodes appeared, which is around 10% of the 2408 nodes included by the
IVAN, and those communities were analyzed as regional communities. Therefore,
the sector-specific European communities shown as gray nodes in Figs 2 and
green small communities in 3 were not treated as the regional community of
Europe. In other words, the European community does not include sector-
specific European communities because Europe has substantial value flows that
have mainly the same type of sector, not different types of sectors.

Originally, the smile curve [41] was viewed in terms of the production stage
of a particular product or its relative position from a specific sector. In a
broad sense, the smile curve in this study appears as a V-shaped curve when
its relative position to the final goods of various sectors is considered as a
whole. Not surprisingly, Helmholtz–Hodge decomposition shows a cross-country
potential flow with high (low) potential in B: mining and quarrying (f:
construction), which is in the upstream (downstream) stage of production. As
seen from the circular relationship, the contributions of B: mining and
quarrying and F: construction to international economic integration also
indicate that the manufacture of each country depends on the resources and
development demands (such as construction) of other countries.

To examine the implications of the economic integration index, we focused on
the period of 2008–2011, which has exhibited substantial changes in economic
integration (Fig 8); we also analyzed 2000 and 2014, which are the first and
last years of the analyzed WIOD. Fig 12 shows the changes in the international
and intersectoral relationships of circular flow in Europe. The circulation in
2008, the year of the highest integration index in Europe for the 15 years, is
higher between Germany, France, Italy, and Russia compared with that in 2000.
However, in 2011 and 2014, which has the lowest economic integration, Russia
is absent in Europe, as shown in Tables 3 and 7. From a sectoral point of
view, Fig 13 shows sector B: mining and quarrying as a hub of sectors F:
construction; C19: manufacture of coke and refined petroleum products; and
D35: electricity, gas, steam, and air conditioning supply. Therefore, the role
of Russia and sector B: mining and quarrying is important for the high
economic integration index in Europe.

Fig 12: International value-added circulation of Europe in 2000, 2008–2011,
and 2014. These graphs illustrate the top 20 links. Their node sizes and link
widths are in proportion to the square root of the degree and the amount of
circular flow, respectively. S1 Table. shows a detailed list of the sectors.
Fig 13: Intersectoral value-added circulation of Europe in 2000, 2008–2011,
and 2014. These graphs illustrate the top 20 links. Their node sizes and link
widths are in proportion to the square root of the degree and the amount of
circular flow, respectively. S2 Table: List of sectors. shows a detailed list
of the sectors.

Figs 14 and 15 show the changes in international and intersectoral
relationships in the Pacific Rim. According to Fig 14, the center of the
value-added circulation in the Pacific Rim changed from the United States and
Japan to the United States and China. This also means that the Pacific Rim, as
a regional community of IVANs, was detected stably because of the strong
value-added circulation around the United States and China despite the
economic crisis around 2009. From the sectoral perspective, Fig 15 shows that
there are three crucial points in the circular structure of the Pacific Rim;
these are the strongest stable circulations from B: mining and quarrying to F:
construction, those within C26: manufacture of computer, electronic, and
optical products, and those within C29: manufacture of motor vehicles, and
trailers and semi-trailers for the years 2000–2014.

Fig 14: International value-added circulation of the Pacific Rim in 2000,
2008–2011, and 2014. These graphs illustrate the top 20 links. Their node
sizes and link widths are in proportion to the square root of the degree and
the amount of circular flow, respectively. S1 Table. shows a detailed list of
the sectors. Fig 15: Intersectoral value-added circulation of the Pacific Rim
in 2000, 2008–2011, and 2014. These graphs illustrate the top 20 links. Their
node sizes and link widths are in proportion to the square root of the degree
and the amount of circular flow, respectively. S2 Table: List of sectors.
shows a detailed list of the sectors.

In Europe, the circulation between sectors B: mining and quarrying and F:
construction is unstable because sector B mainly occurs in Russia, which is
not an EU member country. Therefore, the extent of economic integration tends
to be unstable. By contrast, the Pacific Rim has mineral resources. It also
has neutral- and low-potential sectors with high circulation, namely,
manufacture of high-tech and motor vehicles, respectively, which produces the
high-value-added products as parts of GVCs.

These results suggest that the stable growth of economic integration in the
Pacific Rim has been driven by the relationship of the value-added circulation
of these resources and international division in the manufacture of high
value-added products. Furthermore, in the Pacific Rim, the international
division of labor is advancing, and value-added circulation is occurring
across countries. This can be explained by the fact that, the free movement of
labor in the EU has led to the specialization of sectors; in the Pacific Rim,
the movement of labor is limited, and the international division of labor has
led to the free movement of goods.

## Conclusion

The purpose of this study is to clarify how international economic integration
is occurring from the perspective of trade in value-added. For this purpose,
we used the WIOD from 2016 to construct and analyze IVANs, which show the
international relationship of sector-wise trade in value-added. First, the
scope of economic integration was identified by Infomap, a community detection
method that uses network flows. With threshold setting in the IVANs, regional
communities in Europe and the Pacific Rim were detected throughout the 15
studied years. These two communities have not been found in studies that
analyzed international trade networks constructed from the WIOD. To analyze
how value flows within these two regions, we used Helmholtz–Hodge
decomposition to extract the potential and circular relationships and
clarified the annual changes in the roles played by the countries and sectors
within these regions. In addition, we defined an economic integration index
using the circular flow and applied it to both regions. We found that the
level of economic integration in Europe, which had been increasing until 2008,
dropped sharply after the economic crisis in 2009 to a level lower than that
of the Pacific Rim in 2010, recovered in 2011, and dropped again after 2012 to
a level below that of the Pacific Rim in 2013 and 2014. While the level of
economic integration in Europe has been unstable, that in the Pacific Rim has
been on a stable upward trend.

Moreover, the sectoral economic integration index provides a background to the
changes in the extent of economic integration of these two regions. In Europe,
the extent of economic integration declined in 2009, 2010, and 2013 due to the
decrease of intra-European value-added circulation through the industries of
mining, construction, petroleum, metal, machinery manufacture, wholesale,
financial services, and management services, which showed a large amount of
the circular flow of IVAN. This unstable extent of economic integration in
Europe can be attributed to the fact that the free movement of labor within
the EU has resulted in the connection of value-added circulation in specific
sectors rather than the region as a whole. Meanwhile, in the Pacific Rim,
economic integration is progressing slowly but steadily against the
international vertical division of labor in sectors C26: manufacture of
computer, electronic, and optical products, and C29: manufacture of motor
vehicles. In the Pacific Rim, the international division of labor is believed
to be developing stably because of the limited movement of labor.

## Supporting information

##### S1 Table.

List of countries and regional classification. The table is in Appendix as
Table 15.

##### S2 Table.

List of Sectors. The table is in Appendix as Table LABEL:S2_Tab.

## Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers JP17KT0034.

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## Appendix

Table 15: Country list and regional classification.

ISO code | Short name | Region | ISO code | Short name | Region
---|---|---|---|---|---
AUS | Australia | Pacific Rim | IRL | Ireland | Europe
AUT | Austria | Europe | ITA | Italy | Europe
BEL | Belgium | Europe | JPN | Japan | Pacific Rim
BGR | Bulgaria | Europe | KOR | Korea | Pacific Rim
BRA | Brazil | Pacific Rim | LTU | Lithuania | Europe
CAN | Canada | Pacific Rims | LUX | Luxembourg | Europe
CHE | Switzerland | Europe | LVA | Latvia | Europe
CHN | China | Pacific Rim | MEX | Mexico | Pacific Rim
CYP | Cyprus | Europe | MLT | Malta | Europe
CZE | Czechia | Europe | NLD | Netherlands | Europe
DEU | Germany | Europe | NOR | Norway | Europe
DNK | Denmark | Europe | POL | Poland | Europe
ESP | Spain | Europe | PRT | Portugal | Europe
EST | Estonia | Europe | ROU | Romania | Europe
FIN | Finland | Europe | RUS | Russia | Pacific Rim
FRA | France | Europe | SVK | Slovakia | Europe
GBR | United Kingdom | Europe | SVN | Slovenia | Europe
GRC | Greece | Europe | SWE | Sweden | Europe
HRV | Croatia | Europe | TUR | Turkey | Europe
HUN | Hungary | Europe | TWN | Taiwan | Pacific Rim
IDN | Indonesia | Pacific Rim | USA | America | Pacific Rim
IND | India | Pacific Rim |  |  |

Table 16: S2 Table: List of sectors.

Code | Description
---|---
A01 | Crop and animal production, hunting and related service activities
A02 | Forestry and logging
A03 | Fishing and aquaculture
B | Mining and quarrying
C10 | Manufacture of food products, beverages and tobacco products
C13 | Manufacture of textiles, wearing apparel and leather products
C16 | Manufacture of wood and of products of wood and cork except furniture,
and manufacture of articles of straw and plaiting materials
C17 | Manufacture of paper and paper products
C18 | Printing and reproduction of recorded media
C19 | Manufacture of coke and refined petroleum products
C20 | Manufacture of chemicals and chemical products
C21 | Manufacture of basic pharmaceutical products and pharmaceutical preparations
C22 | Manufacture of rubber and plastic products
C23 | Manufacture of other non-metallic mineral products
C24 | Manufacture of basic metals
C25 | Manufacture of fabricated metal products except machinery and equipment
C26 | Manufacture of computer, electronic, and optical products
C27 | Manufacture of electrical equipment
C28 | Manufacture of machinery and equipment n.e.c.
C29 | Manufacture of motor vehicles, trailers and semi-trailers
C30 | Manufacture of other transport equipment
C31 | Manufacture of furniture, and other manufacturing
C33 | Repair and installation of machinery and equipment
D35 | Electricity, gas, steam and air conditioning supply
E36 | Water collection, treatment and supply
E37 | Sewerage, waste collection, treatment and disposal activities, and materials recovery,
and remediation activities and other waste management services
F | Construction
G45 | Wholesale and retail trade and repair of motor vehicles and motorcycles
G46 | Wholesale trade except that of motor vehicles and motorcycles
G47 | Retail trade except that of motor vehicles and motorcycles
H49 | Land transport and transport via pipelines
H50 | Water transport
H51 | Air transport
H52 | Warehousing and support activities for transportation
H53 | Postal and courier activities
I | Accommodation and food service activities
J58 | Publishing activities
J59 | Motion picture, video and television programme production, sound recording and
music publishing activities; programming and broadcasting activities
J61 | Telecommunications
J62 | Computer programming, consultancy and related activities; information service activities
K64 | Financial service activities, except insurance and pension funding
K65 | Insurance, reinsurance and pension funding except compulsory social security
K66 | Activities auxiliary to financial services and insurance activities
L68 | Real estate activities
M69 | Legal and accounting activities, and activities of head offices, and management
consultancy activities
M71 | Architectural and engineering activities, and technical testing and analysis
M72 | Scientific research and development
M73 | Advertising and market research
M74 | Other professional, scientific and technical activities, and veterinary activities
N | Administrative and support service activities
O84 | Public administration and defense, and compulsory social security
P85 | Education
Q | Human health and social work activities
R_S | Other service activities
T | Activities of households as employers, and undifferentiated goods and services
producing activities of households for own use
U | Activities of extraterritorial organizations and bodies