| Abstract | 第8-9页 |
| 摘要 | 第10-11页 |
| Chapter 1 Background and Preliminary | 第11-19页 |
| 1.1 Background | 第11-16页 |
| 1.2 Notation and terminology | 第16-19页 |
| Chapter 2 A General Dynamical Function Corresponding to Develop-ment Process of Scale-free Networks | 第19-24页 |
| 2.1 Construction of dynamical function | 第19-20页 |
| 2.2 Discussions of some existing models | 第20-22页 |
| 2.3 Discussion | 第22-24页 |
| Chapter 3 Several Stochastic Scale-free Network Models | 第24-29页 |
| 3.1 The Classical BA Scale-free Model | 第24-26页 |
| 3.2 The Double Preferential Scale-free Network Model | 第26-29页 |
| Chapter 4 Study of Some Deterministic Network Models | 第29-45页 |
| 4.1 Operations and Functions among Simpler and Smaller Networks/Graphs | 第29-30页 |
| 4.2 Network Model A | 第30-38页 |
| 4.2.1 Construction | 第30-32页 |
| 4.2.2 Topological properties of the network model N(t) | 第32-38页 |
| 4.2.2.1 Average degree | 第33页 |
| 4.2.2.2 Degree distribution | 第33-34页 |
| 4.2.2.3 Clustering coefficient | 第34-35页 |
| 4.2.2.4 Diameter and average path length | 第35-38页 |
| 4.3 Scale-free Network Model B | 第38-40页 |
| 4.3.1 Construction | 第38-39页 |
| 4.3.2 Properties | 第39-40页 |
| 4.4 Small-world Network Model C | 第40-45页 |
| 4.4.1 Construction | 第40-41页 |
| 4.4.2 Properties | 第41-45页 |
| Chapter 5 A New Method for Computing The Total Number of Span-ning Trees | 第45-51页 |
| 5.1 Introduction of New Method | 第45-47页 |
| 5.2 Brouwer's Fixed Point Theorem | 第47-48页 |
| 5.3 Applications | 第48-51页 |
| Chapter 6 Connection Between Detecting Community Structure andPartitioning Graph | 第51-58页 |
| 6.1 Some Algorithms for Detecting Community Structure | 第52-53页 |
| 6.2 The Connection both Detecting Community Structure and PartitioningGraph | 第53-58页 |
| Chapter 7 Conclusion | 第58-61页 |
| References | 第61-66页 |
| Appendix1 Complementary materials | 第66-76页 |
| Appendix2 Published and Submitted Papers During Graduate StudyPeriod | 第76-80页 |
| Appendix3 Rewards and Main Academic Activities During GraduateStudy Period | 第80-82页 |
| Appendix4 Acknowledgements | 第82-85页 |
| 致谢 | 第85页 |
