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几类复杂网络模型的拓扑性质:小世界无标度特性,生成树的数目和社区结构

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

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