国际贸易网络
樊瑛
北京师范大学系统科学学院
2013.07.08
复杂网络简介
Simple
Complex System
Complicated
Complex systems
Complex Systems
Complex systems are all around us:

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economies
nature: ant, bee, bird colonies
little robots
相互作用与复杂性
晶格
扩散
全局相互作用
平均场
Internet
?
Complex Networks

complex networks are the backbone of
complex systems

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
every complex system is a network of
interaction among numerous smaller elements
understanding a complex system = break down
into parts + reassemble
network anatomy is important to
characterize because structure affects
function (and vice-versa)
为什么研究复杂网络？
• 复杂系统不能够用分析的方法去研究，
必须考虑个体之间的关联和作用；
• 理解复杂系统的行为应该从理解系统相互
作用网络的拓扑结构开始；
• 网络拓扑结构的信息是构建系统模型、研
究系统性质和功能的基础。
为什么研究复杂网络？
复杂网络是研究复杂系统的一种角
度和方法，它关注系统中个体相互关联
的作用的拓扑结构，是理解复杂系统性
质和功能的基础。
复杂网络是对复杂系统的一种抽象
Complex systems
Made of
many non-identical elements
connected by diverse interactions.
NETWORK
复杂网络
同质性？（个体、相互作用）
复杂网络的数学描述



网络G=（V, E），由点集V（G）和边集E（G）组成
的一个图，可分为无向、有向和加权网络
令ei∈ E（G），每条边ei有V（G）中的一对点(u,v)与
之对应；
如果任意(u,v)与(v,u)对应同一条边，则称为无向
网络，否则为有向网络；
如果任意∣ei ∣ =1，则称为无权网络，否则为加权
网络。
链接矩阵及拉普拉斯矩阵
技术网络
WWW
因特网
电力网
社会网络
科学引文网
朋友关系网
演员网
科学家合著网
交通运输网络
城市公共交通网
航空网
道路交通网
生态、生物网络
生态网络
蛋白质相互作用网络
神经网络
基因网络
新陈代谢网络
不同领域的复杂网络
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



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社会网：演员合作网，朋友网，姻亲关系网，
科研合作网，Email网，短信网…
生物网：食物链网，神经网，新陈代谢网，蛋
白质网，基因网络…
信息网络：WWW，专利使用，论文引用，…
技术网络：电力网，Internet，电话线路网，
交通运输网：航线网，铁路网，公路网，自然
河流网
经济系统：投入产出网，国际贸易，…
网络研究的历史

1736，欧拉：哥尼斯堡七桥

1950，Erdos, Renyi: 随机图论

1998，Strogatz； 1999，Barabasi: 小世界
和无标度网络
复杂网络的兴起
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计算机技术的发展：
 使我们有可能对大规模的网络进行实证研究
普适性的发现：
 许多实际网络具有相同的定性性质
 且已有的理论不能描述和解释
理论研究的发展
 小世界网络 (Small World Network), 无标度网络 (Scale-free
Network)
 统计物理学的研究手段
应用领域的丰富
 社会经济系统、生命生态系统等
复杂网络研究所关心的问题
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
如何建立复杂网络？网络研究中的反问题
如何定量刻画复杂网络？

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网络是如何发展成现在这种结构的？

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网络结构的描述及其性质
网络演化模型
网络特定结构的后果是什么？正问题


网络结构的鲁棒性
网络上的动力学行为和过程
国际贸易网络
World Trade Network
Our Global Village
Under the world economy, the trading relation
multiple influence.
The influence can widely transmitted to
other countries.
between countries have
What Is World
Trade Network?
Or International Trade Network, World Trade Web…
Network Construction
Binary
Directed
Weighted
export
All value / the cut-off value
expij
Total Trade
expij
GDPi
or
im pij
(Kastelle et al., 2006; Kastelle, 2009)
(Tzekina et al., 2008; Kali and Reyes, 2007)
Total Trade
(Fagiolo et al., 2007; Fagiolo et al., 2008; Fagiolo et al., 2010)
About World
Trade Network
World Trade Network( 2003-2012 )
Structure and Function
Binary
Weighted
Function
 scale-free degree distribution, the small-world property, a high clustering
coefficient (Serrano and Boguna, 2003);
 disassortative (Garlaschelli and Loffredo, 2005);
 synchronization (Li et al., 2003).
 weakly disassortative (Fagiolo et al., 2008);
 distribution of the total trade intensity(i.e., node strength) is rightskewed (Fagiolo et al., 2008;2009;2010).
 the log-normal distribution of link weights which remains robust over
recent decades (Fagiolo et al., 2009; Bhattacharya et al.,2008);
 the size of the rich-club controlling half of the world’s trade is actually
shrinking (Bhattacharya et al.,2008).
 a ”robust yet fragile” configuration: robust to random failures but fragile
under targeted attack (Foti et al., 2011);
 crisis spreading also dependent on its local and global topology
structure of world economic network (Lee et al., 2011).
See World
Trade Network
2010 World Trade Network in our eyes
Communities
Note:
By using of Weighted Extremal Optimization algorithm and Coarse Graining process
See World
Trade Network
2010 World Trade Network in our eyes
Centrality of Vertices
No
Degree
1
2
3
4
5
6
7
8
9
10
EU
MAL
CHN
ROK
INS
AUL
USA
JPN
IND
BRA
Strength Closeness Eigenvector Betweenness
EU
USA
CHN
JPN
ROK
CAN
MEX
RUS
IND
SIN
EU
CHN
USA
CAN
JPN
MEX
RUS
SWZ
ROK
NOR
USA
CHN
EU
MEX
CAN
JPN
ROK
RUS
SWZ
IND
EU
CHN
USA
JPN
IND
RUS
BRA
SIN
SAF
THI
Community
I
USA
EU
CAN
CHN
JPN
RUS
MEX
SWZ
ROK
TUR
Community
W
SUD
FJI
EGY
YEM
INS
SAU
AUL
EU
CHN
JPN
Bootstrap Percolation on Lattice
Sites’ States:
active “
”
or inactive “
”,
Update Rules:
Initial Active Probability: f
Active Threshold: 
Proportion of Sites are Active: S  f 
a
START
…
f=0.2
2
Sa  f   0.6
First Introduced
Study the diminution and eventual destruction of magnetic order by nonmagnetic impurities in a magnet.
- J. Chalupa, P.L.Leath, G.R.Reich, Bootstrap percolation on a bethe lattice, J.Phys.C: Solid
State Phys. 12 (1979) L31–L35.
Application
An useful model to describe complex phenomena
• The neuronal activity (Eckmann et al., 2007; Soriano et al., 2008; Goltsev et al., 2009);
• Hydrogen mixtures (Adler et al., 1987);
• The dynamics of the glass transition (Nakanishi and Takano,1986;Ertel et al., 1988;
Sellitto et al., 2005; Toninelli et al., 2006);
• The magnetic alloys (Kogut and Leath, 1981).
Bootstrap Percolation on Complex Networks
Vertices’ States:
active “
”
or inactive “
”
Update Rules:
Initial Active Probability: f
Active Threshold: 
Proportion of Sites are Active: S a  f 
f=0.2
START
2
Sa  f   0.6
Bootstrap Percolation on Complex Networks
(G.J. Baxter et al. Phys.Rev.E, 82:011103, 2010.)
Fig. 1. Phase diagram in the f-p plane
networks with finite second moment of the degree distribution
Fig.2. Probability that
an arbitrarily chosen
vertex is (a) active
and (b) in a
giant
connected
component of
active vertices
Erdős-Rényi graph of
mean degree 5, with k=3.
Bootstrap Percolation on Bipartite Networks
(Wan Baohui et al. Acta Phys.Sin., 61(16):166402, 2012.)
Update Rules of Vertex 2
N1=2000,N2=1600
Ώ1=10, Ώ2=9
f1=f2, Ώ1=10
F2=0.2, Ώ1=10, Ώ2=9
Trading relations are so
important !!!
How can we explore the
impact of trading relations?
Basic Assumptions
 Vertices States：
Normal state
Abnormal state
 Transmission in Edges：
Along the country’s commodities and services' export flows.
Country influence system by restricting imports or changing
export.
 Transmission Process：in a short term, discrete in time
 Topology Distance Rather Than Geographical Distance
Rules
Step1
Step2
Step3
Step4

w

For each i, if (Rule.1.) w

k A

ki
ji
ki
 ;
  ;or (Rule.2.)
GDPi
k A
j
it will become abnormal.
w
( A: Abnormal Neighbors)
Case: USA, China and Japan
Final Scope of Impact (Rule.1.)
Case: USA, China and Japan
Final Scope of Impact (Rule.2.)
Case: USA, China and Japan
Phase Transition (Rule.1.)
(a) disconnecting unilateral trading relation
From-to
China-USA
China-Japan
USA-China
USA-Japan
Japan-China
Japan-USA
Ω
0.245
0.221
0.187
0.187
0.208
0.208
Sa
0.923
0.923
0.923
0.923
0.923
0.923
Gap
0.852
0.814
0.743
0.787
0.896
0.896
t
6
7
9
8
10
9
Sa
0.923
0.923
0.923
Gap
0.710
0.776
0.738
t
11
8
10
(b) disconnecting bilateral trading relation
From-to
USA & China
USA & Japan
China & Japan
Ω
0.391
0.295
0.362
Case: USA, China and Japan
Phase Transition (Rule.2.)
(a) disconnecting unilateral trading relation
From-to
China-USA
China-Japan
USA-China
USA-Japan
Japan-China
Japan-USA
Ω
0.120
0.120
0.094
0.095
0.072
0.096
Sa
0.809
0.809
0.918
0.913
0.923
0.902
Gap
0.585
0.585
0.536
0.634
0.634
0.738
t
14
14
13
12
9
10
(b) disconnecting bilateral trading relation
From-to
USA & China
USA & Japan
China & Japan
Ω
0.138
0.126
0.130
Sa
0.874
0.891
0.847
Gap
0.459
0.623
0.530
t
11
9
14
Case: USA, China and Japan
Conclusions
In Our Case:
1
The China’s export to United States and Japan
is even more important.
2
Relations between China, USA and Japan are more
important than random cases. They are important,
too.
Table 1: Phase transition point of disconnecting bilateral trading relation of two-direction (a) and one-direction (b)
between five economies.
(a) two-direction
(b) one-direction
No.
Country
Defense
threshold
No.
Country
Defense
threshold
No.
Country
Defense
threshold
1
EU & USA
0.6205
1
CHN-EU
0.3381
4
USA-ASEAN
0.3173
2
EU & CHN
0.5257
1
CHN-USA
0.3381
5
USA-CHN
0.2928
3
USA & CHN
0.5063
1
CHN-JPN
0.3381
6
JPN-EU
0.2077
4
EU & JPN
0.4213
1
CHN-ASEAN
0.3381
6
JPN-CHN
0.2077
5
EU & ASEAN
0.4165
2
EU-USA
0.3380
6
JPN-USA
0.2077
6
USA & JPN
0.4069
2
EU-ASEAN
0.3380
7
JPN-ASEAN
0.1903
7
CHN & JPN
0.4042
2
EU-JPN
0.3380
8
ASEAN-EU
0.1563
8
CHN & ASEAN
0.4042
3
EU-CHN
0.3234
8
ASEAN-CHN
0.1563
9
USA & ASEAN
0.3977
4
USA-EU
0.3173
8
ASEAN-USA
0.1563
10
JPN & ASEAN
0.2769
4
USA-JPN
0.3173
9
ASEAN-JPN
0.1370
Thank you !