Evolutionary Models and Dynamical Properties of
Complex Networks
Name: Jianguo Liu
University of Shanghai for Science and
Technology
2010-3-24
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Outline
1.
2.
3.
4.
Complex networks analysis by
Citespace
Network evolution models
Dynamical properties on scalefree networks
Personalized recommendation
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1999年-2010年发表的以“complex networks”为主
题词的SCI论文数
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published SCI
papers
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1999
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Citespace软件介绍
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与技术学院的陈超美开发。该程序可以登录
到cluster.cis.drexel.edu/~cchen/citespace后
免费使用。
 利用Citespace寻找某一
学科领域的研究进展和当
前的研究前沿，及其对应
的基础知识。
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复杂网络论文作者合作网(1999-2010)
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复杂网络研究小组状况(1999-2010)
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复杂网络各个国家研究状况(19992010)
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利用引文分析观察当前的研究热点
(1999-2010)
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Top cited authors(1999-2010)
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各研究领域之间的关系(1999-2010)
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个性化推荐的知识图谱
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Top cited authors
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目前的研究热点
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Outline
1.
2.
3.
4.
Background introduction
Network evolution models
Dynamical properties on
scale-free networks
Personalized
recommendation
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2.Scale-free Network Evolution
Models
1.
2.
3.
4.
Multistage random growing small-world networks with powerlaw degree distribution
Growing scale-free network model with tunable assortative
coefficient
Self-learning mutual selection model for weighted networks
Random evolving networks under the diameter and dverage
connectivity constraint
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2.1.Multistage random growing small-World networks
with power-law degree distribution
•One node is added in each time step；
•Select the node u according to the
preferential mechanism；
•Select a neighbor node of node u；
Liu Jian-Guo, Dang Yan-Zhong and Wang Zhong-Tuo,
Chinese Physics Letters 23(3) 746-749 (2006)
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2.2. Growing scale-free network model with
tunable assortative coefficient
1. One node is added in each time step；
2. Select the node u according to the preferential mechanism；
3. Select a neighbor node of node u according to ps；
Qiang Guo, Tao Zhou, Jian-Guo Liu et al., Physica A 371 814822 (2006)
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2.3 Self-learning mutual selection model for
weighted networks
Two parameters: attractive factor p, the number of candidates m
m=2
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1
1
2
2
3
5
1
3
4
i j 
2
sj  a
 k sk  a
s  s 1
3
4
4
1 p
p
Jian-Guo Liu et al., DCDIS B Supplement, Complex Networks, 14 (S7)
33-36, (2007).
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2.4 Random Evolving Networks Under the Diameter and
Average Connectivity Constraint
The growth of random networks under the constraint
that the diameter, defined as the average shortest path
length between all nodes, and the average connectivity
remains approximately constant is studied. We showed
that, if the network maintains the form of its degree
distribution and the maximal degree is a N-dependent
cutoff function, then the degree distribution would be
approximately power-law with an exponent between 2
and 3.
Jian-Guo Liu et al., Journal of System Science and System
Engineering 16(1) 107-112 (2007).
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Motivation
In the biological networks, the constant diameter may be
related to important properties of these biological networks,
such as the spread and speed of responses to perturbations. In
the Internet backbone network, the average distance is one of
the most important factors to measure the efficiency of
communication network, and it plays a significant role in
measuring the transmission delay. These constraints can be
thought of as the environmental pressures, which would select
highly efficient structure to convey the packets in it.
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Motivation
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Construction of the model

The expression for the diameter d of a random
network with arbitrary degree distribution was
developed

Where
is the average degree,
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In order to seek a degree distribution that maintains its
distribution and has an approximately constant diameter
independent of N. The parameter N can be accomplished by
imposing a N-dependent cutoff function
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
The distribution p(k) can be determined by writing this
equation for
and
Algebraic manipulation
yields the relation
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
Using an integral approximation , a more explicit
formulation can be written as following.
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When
the numerically calculated
degree distributions for various values of
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Discussion of part two
We have presented a reason for the existence of
power-law degree distribution under the diameter
constraint observed in the Internet backbone
network where there are evolutionary pressures to
maintain its diameter. Our analysis shows that, if the
maximal degree is a N-dependent cutoff function, the
form of a robust network degree distribution should
be power law to maintain its diameter, while the
average connectivity per node affect the distribution
exponent slightly.
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Outline
1.
2.
3.
4.
Background introduction
Network evolution models
Dynamical properties on
complex networks
Personalized
recommendation
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3.1 Structural effects on synchronizability of scalefree networks
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3.1 How to measure the synchronizability
Where Q is the ratio of the eigenvalues. The synchronizability
would be increased as Q decreases, vice verse.
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The edge exchange method is introduced to
adjust the network structure, and the tabu search
algorithm is used to minimize the eigenvalue ratio
Q
min
Qiang Guo, Liu Jian-Guo, et al, Chinese Physics Letters 24 (8)
(2007) 2437-2440.
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In summary, using the tabu optimal algorithm, we have optimized
network synchronizability by changing the connection pattern between
different pairs of nodes while keeping the degree distribution. Starting
from scale-free networks, we have studied the dependence between the
structural characteristics and synchronizability. The numerical results
suggest that a scale-free network with shorter path length, lower degree
of clustering, and disassortive pattern can be easily synchronized.
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3.1 Structural effects on synchronizability
Combining the tabu search (TS) algorithm and the edge exchange
method, we enhance and weaken the synchronizability of scale-free
networks with degree sequence fixed to find the structural effects of
the scale-free network on synchronizability
min
max
Liu Jian-Guo, et al, International Journal of Modern Physics C 18(7)
1087-1094 (2008).
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The numerical results indicate that D, C, r and Bm influence
synchronizability simultaneously. Especially, the synchronizability
is most sensitive to Bm.
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Effect of the loop
structure on
synchronizability
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Outline
1.
2.
3.
4.
Background introduction
Network evolution models
Dynamical properties on
complex networks
Personalized recommendation
39
Personalized recommendation



Improved collaborative filtering algorithm based
on information transaction.
Ultra accuracy recommendation algorithm by
considering the high-order user similarities
Effect of user tastes on personalized
recommendation
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Why recommend
We face too much data and sources to be able to find out those most relevant for us.
Indeed, we have to make choices from thousands of movies, millions of books,
billions of web pages, and so on. Evaluating all these alternatives by ourselves is
not feasible at all.
As a consequence, an urgent problem is how to automatically find out the relevant
objects for us.
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Collaborative filtering algorithm
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Herlocker et al., ACM Trans. Inf. Syst. 22: 5-53 (2004)
Content-based algorithm
The user will be
recommended items
similar to the ones
this user preferred in
the past
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Pazzani & Billsus, LNCS 4321: 325-341 (2007)
Improved collaborative filtering algorithm based on
information transaction
In traditional CF algorithm, Firstly, the user similarity is
computed based on the Pearson coefficient

n
s 
p
ij
l 1
ali alj
min{ k (ui ), k (u j )}
Then give the predicted score to the uncollected objects
based on the user similarities
n
vij 
s a
l 1
m
li
jl
s
l 1
li
By using the diffusion process to compute the user
similarity to improve CF algorithm
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Iliustration of the diffusion-based user similarity
The target user is activated and be assigned a unit
recommendation power, then the mass is diffused from
the target user to the objects he has collected, then the
it’s diffused back from the objects to the users.
Jian-Guo Liu et al, International Journal of Modern Physics C 20 285 (2009) .
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Two improved algorithms

We argue that the potential role of the object
degrees should be taken into account to
regulate the user similarity

Only the top-N most similar users’ opinion are
taken into account to save the memory and
increase the computation speed.
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Numerical results of the average
ranking score
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Diversity
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Average ranking score of the topN algorithm
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Conclusion and discussions




Using the diffusion process to compute the user similarity
could improve CF algorithmic accuracy
The computational complexity of the presented algorithm is
much less than that of the standard CF.
Both the two modified algorithm can further enhance the
accuracy.
With properly choice of the parameter N, top-N algorithm
can simultaneously reduces the computational complexity
and improves the algorithmic accuracy.
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2,Ultra accuracy recommendation algorithm by considering
the high-order user similarities
The main idea
Figure 1 shows an illustration, where 1 denotes the
mainstream preference shared by all A, B and C, and
2 is the specific preference of A and C. Both 1 and 2
contribute to the correlation between A and C. Since 1
is the mainstream preference, it also contributes to
the correlations between A and B, as well as B and C.
Tracking the path A to B to C, the preference 1 also
contributes to the second-order correlation between A
and C. Statistically speaking, two users sharing many
mainstream preferences should have high secondorder correlation, therefore we can depress the
influence of mainstream preferences by taking into
account the second-order correlation.
Jian-Guo Liu et al, Physica A 389 881 (2010) .
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The presented algorithm

Denote the user similarity matrix is S
where H is the newly defined correlation matrix,
S={ sij} is the first-order correlation defined as
Eq.(2), and  is a tunable parameter. As discussed
before, we expect the algorithmic accuracy can be
improved at some negative  .
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Numerical results
r
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Effect of user tastes on personalized
recommendation
We study the effects of user tastes on the massdiffusion-based personalized recommendation
algorithm, where a user's tastes or interests are
defined by the average degree of the objects he has
collected. We argue that the initial recommendation
power located on the objects should be determined by
both of their degree and the users' tastes. By
introducing a tunable parameter, the user taste effects
on the configuration of initial recommendation power
distribution are investigated.
Jian-Guo Liu et al, International Journal of Modern Physics C 20 285 (2009) .
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Numerical results
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Achievements

Selected Publications
All publications has been cited over 118. H-index is 7

Phys. Rev. E 80, 017101(2010); 74, 056109 (2006).
Physica A 389, 881 (2010); 371, 861 (2007); 366, 578 (2006); 371, 814 (2006); 377, 302
(2007).
European Physics Journal B 66, 557 (2008);
Int. J. Mod. Phys. C 18 1087 (2008); 20, 285(2009); 20, 1925 (2009); 18, 1087 (2007); 18,
294 (2007).
Chin. Phys. Lett. 25, 773 (2008); 25, 2718 (2008); 23, 746 (2006); 377, 302 (2007); 23,
2327 (2006); 24, 2437 (2007);
Mod. Phys. Lett. B 19, 785 (2005); 20 815 (2006);
Int. J. Syst. Sci. and Syst. Engi. 16, 107 (2007);
J. Comp. & Appl. Math. 181, 252 (2005)
PNAS， 107，4511 (2010)
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Future works

实证数据分析
 大规模数据分析，例如在线社区，手机通讯等。细致研
究数据的统计特性，例如胡海波发现虚拟社会网络的度
度相关性是负值，明显不同于真实的社会网络。张国清
和周涛则发现AS系统的增长也满足Moore定律，互联网
内核比较稳定。

网络通缉特性与个性化推荐效果之间的关联关系研
究
 度量二部分网络的统计指标，找到这些指标，尤其是推
荐多样性之间的关系。
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Many thanks
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