复杂网络引论 : 模型、结构与动力学

Part I Fundamental Theory

Chapter 1 Introduction

1.1 Background and Motivation

1.2 A Brief History of Complex Network Research

1.2.1 The Konigsburg Seven-Bridge Problem

1.2.2 Random Graph Theory

1.2.3 Small-World Experiment

1.2.4 Strength of Weak Ties

1.2.5New Era of Complex-Network Studies

1.3 Some Basic Concepts

1.3.1 Graph Representation of Networks

1.3.2 Average Path Length

1.3.3 Clustering Coefficient

1.3.4 Degree and Degree Distribution

1.3.5 Statistical Properties of Some Real-World Complex Networks

Problems

References

Chapter 2A Brief Introduction to Graph Theory

2.1 What is a Graph?

2.2 Notation, Definitions and Preliminaries

2.3 Eulerian and Hamiltonian Graphs

2.3.1 Eulerian Graphs

2.3.2 Hamiltonian Graphs

2.4The Chinese Postman Problem

2.5 The Shortest Path Length Problem

2.6 Trees

2.7 The Minimum Connector Problem

2.8 Plane Graphs and Planar Graphs

2.9 Euler Formula for Plane Graphs

2.10 Directed Graphs

Problems

References

Chapter 3 Network Topologies： Basic Models and Properties

3.1 Introduction

3.2 Regular Networks

3.3 Random-Graph Networks

3.4 Small-World Network Models

3.4.1 The WS Small-World Network Model

3.4.2 The NW Small-World Network Model

3.4.3 Statistical Properties of Small-World Network Models

3.5 The Navigable Small-World Network Model

3.6 Scale-Free Network Models

3.6.1 The BA Scale-Free Network Model

3.6.2 Robustness versus Fragility

3.6.3 Modified BA Models

3.6.4 A Simple Model with Power-Law Degree Distribution

3.6.5 Local-World and Multi-Local-World Network Models

Problems

References

Part II Applications： Selected Topics

Chapter 4 Internet： Topology and Modeling

4.1 Introduction

4.2 Topological Properties of the Internet

4.2.1 Power-Law Node-Degree Distributions

4.2.2 Hierarchical Structures

4.2.3 Rich-Club Structure

4.2.4 Disassortative Property

4.2.5 Coreness and Betweenness

4.2.6 Growth of the Internet

4.2.7 Router-Levellnternet Topology

4.2.8 Geographic Layout of the Internet

4.3 Random-Graph Network Topology Generator

4.4 Structural Network Topology Generators

4.4.1 Tiers Topology Generator

……

Index

《复杂网络引论：模型、结构与动力学（英文版）》是为自然科学、数学和工程领域的研究生以及本科高年级学生编写的一本入门教科书，可以作为一个学期教学使用的讲义，也可以作为科研参考书或自学读物。《复杂网络引论：模型、结构与动力学（英文版）》力求正确和准确，但并不刻意采取十分严谨的写法，以期通俗易懂，侧重于主要思想和基本方法的介绍，仅提供启发性的数学支撑，希望具有初等微积分、线性代数和常微分方程的读者能够轻松地学习书中的主要内容。
全书分成两大部分：第一部分是基础理论，包括背景材料和信息并附有适量的练习题，旨在让读者熟悉一些最基本的建模方法和分析技巧。第二部分是应用选题，包括复杂网络在几个代表性领域中的应用研究，这些章节彼此相对独立。最后一章是近年来比较活跃的几个前沿研究课题的简介。各章均附有详细的关键文献，希望能够帮助有兴趣的读者很快地进入这些研究领域。