臺灣博碩士論文加值系統

The main purpose of this paper is to find some statistical properties of social networks to enhance further studies on detailed properties of such networks. Except the degree distribution index, we define the efficiency index to achieve our goal. In general, our efficiency index could be applied to social networks with rapid decay in information transmission. Besides, it has several advantages and could help us to analyze the statistical and topological properties of the networks. Furthermore, we find that there exists an optimal process to improve efficiency of the networks and give an explanation about the reason why social planner always chooses the policy of adding one link to any real networks to improve efficiency.

Abstract I
Contents II
1. Introduction 1
2. Basic Notations 5
2.1. Degree distribution 5
2.2. Average path length 6
2.3. Clustering coefficient 6
2.4. Density 7
3. The Efficiency 8
3.1. Global efficiency 8
3.2. Local efficiency 13
4. Analyzing Networks 15
4.1. Statistical properties 15
4.2. Topological properties 16
4.3. Optimality 19
5. Conclusion 24
6. Appendix 26
7. References 32

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