This book is written as a one-semester introductory text for upper-division undergraduate or first-year graduate students in natural science, mathematics and engineering, or as an edited volume for self-study, or as a handy reference for research.
The book is divided into two parts: Part I Fundamental Theory is a detailed text consisting of three chapters, presenting background information and basic materials needed to learn the subject, with a variety of exercises for illustrating fundamental concepts and familiarizing related modeling and analysis techniques. Part II Applications – Selected Topics contains several selected application-oriented topics, which are all independent of each other, in the sense that one can choose any chapters to teach or to learn individually without referring to the contents of the other chapters in this part. The last chapter of this part provides only outlines of several emerging topics which are believed important and promising, with sufficient numbers of key references provided for interested readers’future studies.
目录
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
