Evolutionary Models and Dynamical Properties of Complex Networks

1. Evolutionary Models and Dynamical Properties of Complex Networks Name: Jianguo Liu University of Shanghai for Science and Technology 2010-3-24

2. Outline • Complex networks analysis by Citespace • Network evolution models • Dynamical properties on scale-free networks • Personalized recommendation

3. 1999年-2010年发表的以“complex networks”为主题词的SCI论文数

4. Citespace软件介绍 • CiteSpace：由美国德雷赛尔大学信息科学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。

5. 复杂网络论文作者合作网(1999-2010)

6. 复杂网络研究小组状况(1999-2010)

7. 复杂网络各个国家研究状况(1999-2010)

8. 利用引文分析观察当前的研究热点(1999-2010)

9. Top cited authors(1999-2010)

10. 各研究领域之间的关系(1999-2010)

11. 个性化推荐的知识图谱

12. Top cited authors

13. 目前的研究热点

14. Outline • Background introduction • Network evolution models • Dynamical properties on scale-free networks • Personalized recommendation

15. 2.Scale-free Network Evolution Models • Multistage random growing small-world networks with power-law 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

16. 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)

18. 2.2. Growing scale-free network model with tunable assortative coefficient • One node is added in each time step； • Select the node u according to the preferential mechanism； • Select a neighbor node of node u according to ps； Qiang Guo, Tao Zhou, Jian-Guo Liu et al., Physica A 371 814-822 (2006)

20. 5 1 2 3 4 2.3 Self-learning mutual selection model for weighted networks Two parameters: attractive factor p, thenumber of candidates m m=2 5 1 1 2 2 3 3 4 4 Jian-Guo Liu et al.,DCDIS B Supplement, Complex Networks, 14 (S7) 33-36, (2007).

22. 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).

23. 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.

24. Motivation

25. 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,

26. 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

27. The distribution p(k) can be determined by writing this equation for and Algebraic manipulation yields the relation

28. Using an integral approximation , a more explicit formulation can be written as following.

29. When the numerically calculated degree distributions for various values of

30. 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.

31. Outline • Background introduction • Network evolution models • Dynamical properties on complex networks • Personalized recommendation

32. 3.1 Structural effects on synchronizability of scale-free networks

33. 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.

34. 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.

35. 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.

36. 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).

37. The numerical results indicate that D, C, r and Bm influence synchronizability simultaneously. Especially, the synchronizabilityis most sensitive to Bm.

38. Effect of the loop structure on synchronizability

39. Outline • Background introduction • Network evolution models • Dynamical properties on complex networks • Personalized recommendation

40. 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

41. 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.

42. Collaborative filtering algorithm Herlocker et al., ACM Trans. Inf. Syst. 22: 5-53 (2004)

43. Content-based algorithm The user will be recommended items similar to the ones this user preferred in the past Pazzani & Billsus, LNCS 4321: 325-341 (2007)

44. Improved collaborative filtering algorithm based on information transaction In traditional CF algorithm, Firstly, the user similarity is computed based on the Pearson coefficient Then give the predicted score to the uncollected objects based on the user similarities By using the diffusion process to compute the user similarity to improve CF algorithm

45. 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) .

46. 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.

47. Numerical results of the average ranking score

48. Diversity

49. Average ranking score of the top-N algorithm

50. 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.