hybrid ecological network and flow distance analysis for international oil trade

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Energy Procedia 104 (2016) 209 – 214

CUE2016-Applied Energy Symposium and Forum 2016: Low carbon cities & urban
energy systems

Hybrid ecological network and flow-distance analysis for
international oil trade
Saige Wanga, Bin Chena*
a

State Key Joint Laboratory of Environmental Simulation and Pollution Control, School of Environment, Beijing Normal University,
Beijing 100875, P.R. China

Abstract

International energy interdependency has been increasing with growing energy trade activities, in which
the uneven distributions of energy production and consumption have shaped a structural global market.
In this paper, we build a system-oriented network model with ecological network analysis (ENA) to
address the roles of countries and their interactions in the international oil trade market. The oil trade
flows between countries are calculated, and the control and dependence relationships are explored to
reveal the structural properties. Moreover, flow-distance analysis (FDA) is introduced to elucidate the
hierarchal level of various countries in the international oil market. The results of ENA show that the
control degrees of the US over Canada, Canada over the US, Middle East over India, Australasia over
Europe and Other Asia Pacific over Singapore are strong, and the dependence degrees of the US over
Canada, Canada over the US, Singapore over Middle East, Singapore over Former Soviet Union are also
strong. It can be concluded that the Europe, US and China are the main components consuming the
largest quantity of oil and play important roles in the oil trade network.
Keywords: Energy trade; Ecological network analysis; Flow distance; International oil trade markets

* Corresponding author. Tel/fax.: +86 10 58807368.
E-mail address: (Bin Chen)

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
( />Peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, CUE2016: Low carbon cities
and urban energy systems.
doi:10.1016/j.egypro.2016.12.036


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Saige Wang and Bin Chen / Energy Procedia 104 (2016) 209 – 214

1. Introduction
Since countries have become increasingly interconnected in the globalizing world, the uneven
distributions of oil resources can be mitigated by energy imports and exports via the international energy
trade network [1-2].
Complicated relationships among countries in the international oil trade have shaped a huge and
complex network [3]. Currently, network methods have been introduced to investigate the international
oil trade relations [4–6]. For example, Gao et al. [1] built the international fossil energy trade multilayer
network and explored the evolutionary characteristics of networks via several important indicators,
including degree distribution, community, stability of communities. Zhong et al. [7] and Zhang et al. [8]
further introduced complex network to analyze the competition between countries in the oil trade.
Ecological network analysis (ENA), emphasizing the direct and indirect relationship and interaction
between the key components of the system, can explore the control and dependence relationship
between components, and also identify the critical nodes and flow pathways in the networks [9]. It has
been widely used to reveal the patterns of social-economic systems, and is expected to be applied to oil
trade market.
The flow-distance analysis has been used to rank the nodes and explore the role and position of the

node in the network [10–11], thus reflecting the intrinsic properties of the system. For example, Guo et
al. derived novel explicit expressions of flow distances for open flow networks according to their
underlying Markov matrix of the network [12]. Combining the open flow network with flow-distance
analysis, the economic input-output trade network is investigated to rank sectors according to average
flow distances, and cluster sectors into different industrial groups with strong connections. Shen et al.
established international trade model based on the source and sink node from two coupled viewpoints:
the viewpoint of trading commodity flow and that of money flow, and introduced the concepts of trade
trophic levels and niches, countries’ roles and positions in the global supply chains [13].
In this paper, we built the international oil trade network (IOTN) by incorporating the source and sink
node into the ENA for the oil trade system including 14 countries and regions. Then, we explored the
direct and indirect flows between components via the control and dependence relationship analysis.
Finally, the first-passage flow distance, total flow distance and symmetric flow distance among
components are defined and calculated based on flow-distance analysis.
2. Material and Methods
2.1 International oil trade modeling
The IOTN is established by calculating the energy flow between countries and regions, which
includes 14 common nodes. The fundamental flow matrix F can be written as an adjacency matrix.

F

^F `
i, j

N  2
u N  2


; i, j ^0,1, , N  1`

(1)

where Fi , j is the flow from the ith node to the j th node. Details can refer to the work of Shen et al. [11].


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Saige Wang and Bin Chen / Energy Procedia 104 (2016) 209 – 214

The integral flow is used to explain the influence that one component exerts on another within the
overall system configuration. Here we use N to reflect the direct flows, and NĄ for indirect flows
through the system.
f

N = (nij ) = ¦ G n =(I - G )-1

(2)

n=0

f

N c = (nijc ) = ¦ Gcn =(I - Gc)-1

(3)

n=0

where N = (nij ) is the integral dimensionless matrix of metabolic flows; G ( gij ) is the direct
dimensionless matrix of metabolic flow;

gij =fij / Ti ; fij

refers to oil trade flow from the ith sector to the j
n

th sector; Ti refers to the total through flow of the ith node;

TST

¦ T is the total input/output of the
i

i 1

entire system.
Network control analysis (NCA) can evaluate the dominance of one component over another via
pairwise environs, which is often utilized to represent the micro–dynamics of components. Combing
two integral matrices N and N c , we may calculate the CA and DA to quantify the control and
dependence relationships between nodes [12].
CR nij  n ji '
­
°nij  n ' ji ! 0,
CA=(caij ) { ®
°n  n ' d 0,
ji
¯ ij

­
°nij  n ' ji ! 0,
DA=(daij ) { ®

°n  n ' d 0,
ji
¯ ij

(4)
caij
caij

daij
daij

nij  n ' ji
max(nij , n ' ji )
0

(5)
nij  n ' ji
max(nij , n ' ji )
0

(6)

2.2 Flow-distance analysis
In ENA, the matrix Am gives exactly the number of paths between two nodes of length m, which is
used to measure system hierarchical structure and indirectness between nodes, in which A1 are the direct
paths, A2 are the paths that take two steps, A3 are the paths that take three steps, etc. Similarly, the mean
D
first-passage flow distance (MFPFD) from the ith node to the j th node (denoted as lij is defined as the

expected number of steps for reaching j for the first time, given that initially the particles are at i. The

D

mean total flow distance (MTFD) (denoted as tij ) is the average number of steps for arriving at j [12].
2.3 Data Sources


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Data used in this study come from four sources including the bilateral trade database from the global
trade analysis project (GTAP) [13], the World Development Indicators (World Bank, 2014) [14] and the
BP energy statistics (BP, 2014) [15]. The trade volumes are measured by Million tones.
3. Results
The control and dependence relationships among components of international oil trade systems is
shown in Fig.1. The control of the US over Canada, Canada over the US, Former Soviet Union over
Europe, Middle East over India, Australasia over Europe and Other Asia Pacific over Singapore is
strong, whose CA values are above 0.5. That means countries and regions who have high control over
others will great affect the others. Especially, the US and Canada have strong control between each
other, implying that these two countries have strong interactions in oil trade. The dependence of the US
over Canada, Canada over the US, Singapore over middle east, Singapore over Former Soviet Union are
strong, whose DA values are above 0.5, which means countries and regions that have high dependences
over the others, would have high reliance over the corresponding ones.

a. CA

b. DA

Fig. 1 Control and dependence relationships among countries and regions of international oil trade network.
Note: 1, The US; 2, Canada; 3, Mexico; 4, South & Central America; 5, Europe; 6, Former Soviet Union; 7, middle east; 8,

Africa; 9, Australasia; 10, China; 11, India; 12, Japan; 13, Singapore; 14, Other Asia Pacific.

Fig. 2 shows the oil trade interaction among the components including 14 countries and regions.
According to the width of flows, we can identify the amount of the flow between components. The
directions of flows can highlight the role of the component play in the international oil trade network.
From the directions of the flows, it can be concluded that the Europe, US and China are the main
components consuming the largest quantity of oil and playing important roles in the international oil
trade network. Also, the components provide largest amount of transferring flows for each country and
region. For example, the components that provide largest amount of transferring flows for Middle East
are the Other Asia Pacific, China and Europe.


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Saige Wang and Bin Chen / Energy Procedia 104 (2016) 209 – 214

Fig. 2 Oil trade flows in international oil trade network.
Note: USA, The US; CAN, Canada; MEX, Mexico; SCA, South & Central America; EU, Europe; FSU, Former Soviet Union;
ME, middle east; AUS, Australasia; CHN, China; IND, India; JPN, Japan; SG, Singapore; OAP, Other Asia Pacific.

Fig. 3 illustrates the international oil trade network between 14 countries and regions. As we can see,
the US, Middle East, South & Central America and China are active in the international oil trade
network.

6

2

5
1

1 USA

12
10

2 Canada
3 Mexico

7

3

11

4 S. & Cent. America
5 Europe
6 The Russian Federation
7 The Middle East

14

4

8 Africa

9 Australia

8

13

9

10 China
11 India
12 Japan
13 Singapore

14 Other Asia Pacific countries

Fig. 3 International oil trade network between 14 countries and regions.

4. Conclusion
In this paper, the IOTN is established based on ENA. The control and dependence relationship between
regions are explored via ENA. The first-passage flow distance, total flow distance and symmetric flow
distance among components are also defined and calculated based on flow-distance analysis to elucidate
the roles and positions of regions in international oil trade market. It is concluded that controls of the US
over Canada, Canada over the US, Former Soviet Union over Europe, Middle East over India, Australasia
over Europe and Other Asia Pacific over Singapore are strong, and the dependences of the US over
Canada, Canada over the US, Singapore over Middle East, Singapore over Former Soviet Union are


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Saige Wang and Bin Chen / Energy Procedia 104 (2016) 209 – 214

strong. The Europe, US and China are the main components and play important roles in the international
oil trade network.
Acknowledgement

This work was supported by the National Key Research & Development Program (2016YFA0602304),
National Natural Science Foundation of China (No. 71573021, 71628301), Specialized Research Fund for
the Doctoral Program of Higher Education of China (No. 20130003110027), and China-EU Joint Project
from Ministry of Science and Technology of China (No. SQ2013ZOA000022).
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