||Modeling and Simulation of Social Networks
||Department of Computer Science and Information Engineering
Social network model
在社群網路模型中，大家著重關注的是網路中的叢集度(clustering coefficient)及無尺度(scale-free)特性。在2005年時，加州理工學院的Lun Li等人提出了對於s-metric的觀察，這是對於網路中高連結節點與其他高連結節點彼此連結程度的觀察指標。我們所提出的新模型即針對此點來做加強。
在這篇論文中，我們提出了兩個社群網路模型，一是基於穴居人網路(caveman network)的靜態模型，一是基於成長網路(growing network)的動態模型。在模擬中，我們的網路模型都能提供叢集度及無尺度的特性，對於s-metric，亦有非常好的效果。同時，我們從Internet上取得了三個實際社群網路資料來做實驗比對，在模擬實驗中，雖然無法找到完全符合的參數，但亦提供了相當好的參考。
||The social network model has been used for the simulation of epidemiological transmission, rumor spreading, opinion formation, and the spread of computer viruses in email network. Since social networks can be found in many aspects of our lives, it is worth to investigate how they work precisely.
The study suggests two models for social network based on a caveman network and growing network. The models we propose can fit the following two properties basically: (1) 'scale-free property' which has power law degree distribution, and (2) 'small-world property' which has high clustering coefficient. In addition, the models are modified for high hub connectivity which is a new viewpoint in scale-free network. This study also provided some empirical data for analysis.
List of Figures III
List of Tables VI
CHAPTER 1 Introduction 1
CHAPTER 2 Background Knowledge 3
2.1 Scale-Free 3
2.2 Small-World 4
2.3 S-metric 6
CHAPTER 3 Related Works 8
3.1 The Evolution of the Social Network of Scientific Collaborations 8
3.2 The Highly Clustered Scale-Free Networks 9
3.3 The Growing Scale-Free Networks with Tunable Clustering 10
3.4 The Growing Scale-Free Networks with Small-World Behavior 10
3.5 The Geography in a Scale-Free Network Model 11
3.6 The Structure of a Large Social Network 11
3.7 The Models of Social Networks Based on Social Distance Attachment 12
3.8 The Evolving Scale-Free Network Model with Tunable Clustering 12
3.9 A Spatial Model for Social Networks 13
3.10 A Model for Social Networks 14
3.11 Summary 14
CHAPTER 4 Empirical Networks 15
4.1 The Opel Astra Club (OAC) 15
4.2 The Mygrizzie Website (Grizzie) 15
4.3 The People Fisher Website (PFW) 16
4.4 Empirical results 16
CHAPTER 5 New Models 21
5.1 Static Model 21
5.2 Dynamic Model 23
CHAPTER 6 Simulation 26
6.1 Static Model 26
6.2 Dynamic model 32
CHAPTER 7 Conclusions and Future Works 45
Publication List 51
List of Figures
Figure 1. Random rewiring procedure between a regular ring lattice and a random network. 6
Figure 2. The log-log degree distribution plot of the OAC, the slope of the line is -1.232. 17
Figure 3. The log-log degree distribution plot of the Grizzie, the slope of the line is -1.198. 18
Figure 4. The log-log degree distribution plot of the PFW, the slope of the line is -1.292. 18
Figure 5. The log-log rank versus degree distribution plot of OAC. 19
Figure 6. The log-log rank versus degree distribution plot of Grizzie 19
Figure 7. The log-log rank versus degree distribution plot of PFW. 20
Figure 8. Left is an initial caveman network with n=30 and w=5. Right is after added edges. 23
Figure 9. The double circle nodes are the neighbor nodes of PA or FA. (a) is FA1 connects to the neighbor node of PA1; (b) is FA2 connects to the neighbor node of PA3; (c) is FA3 connects to the neighbor node of FA2; (d) is FA4 connects to the neighbor node of FA3. 25
Figure 10. The clustering coefficient when degree k=6 to 12. 28
Figure 11. The tail index when degree k=6 to 12. 28
Figure 12. The average distance L when degree k=6 to 12. 29
Figure 13. The s(g)/smax when degree k=6 to 12. 30
Figure 14. The log-log degree distribution plots, the parameters are w=3, k=12, (a) n=900, (b) n=3000, (c) n=9000, (d) n=15000. 30
Figure 15. The log-log rank versus degree distribution plots, the parameters are w=3, k=12, (a) n=900, (b) n=3000, (c) n=9000, (d) n=15000. 31
Figure 16. The log-log degree distribution plot of our dynamic model with N=866, k=8.907, f=0.30, x=0.40. The slope of the line is -1.342. 33
Figure 17. The log-log degree distribution plot of our dynamic model with N=1975, k=7.764, f=0.35, x=0.20. The slope of the line is -1.507. 34
Figure 18. The log-log degree distribution plot of our dynamic model with N=2738, k=6.817, f=0.35, x=1.0. The slope of the line is -1.285. 34
Figure 19. The value of S with N=2738, f=0.05~0.55. The average degree k by (12) in the constructed network before extra edges added is 5.991, and the others after edges added by (13) are 6.817. 37
Figure 20. The clustering coefficient C with N=2738, f=0.05~0.55. The average degree k by (12) in the constructed network before extra edges added is 5.991, and the others after edges added by (13) are 6.817. 37
Figure 21. The tail index with N=2738, f=0.05~0.55. The average degree k by (12) in the constructed network before extra edges added is 5.991, and the others after edges added by (13) are 6.817. 38
Figure 22. The S with N=2000, m=3, f=0.10, and the extra edges added are from 100 to 1000. 39
Figure 23. The clustering coefficient C with N=2000, m=3, f=0.10, and the extra edges added are from 100 to 1000. 39
Figure 24. The tail index with N=2000, m=3, f=0.10, and the extra edges added are from 100 to 1000. 40
Figure 25. The log-log degree distribution plots, the parameters are f=0.5, x=0.8, k=12, (a) n=900, (b) n=3000, (c) n=9000, (d) n=15000. 40
Figure 26. The log-log rank versus degree distribution plots, the parameters are f=0.5, x=0.8, k=12, (a) n=900, (b) n=3000, (c) n=9000, (d) n=15000. 41
Figure 27. The OAC network topology. 42
Figure 28. The static model topology with N=864,w=4. 43
Figure 29. The dynamic model topology with N=866,m=4, f=0.3, x=0.3. 44
List of Tables
Table 1. The algorithm of calculating smax in a simple graph. 7
Table 2. The empirical data of the three real networks 20
Table 3. The comparison with three models when adding one new node. 25
Table 4. The static model simulation results with OAC, Grizzie and PFW. 29
Table 5. The s(g)/smax in multi graph and s(g)/smax in simple graph. 31
Table 6. The comparison between OAC and simulation of dynamic model. 35
Table 7. The comparison between Grizzie and simulation of dynamic model. 36
Table 8. The comparison between PFW and simulation of dynamic model. 36
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