Book:Maarten van Steen/Graph Theory and Complex Networks

Subject Matter

 * Graph Theory

Contents

 * Preface


 * 1 Introduction
 * 1.1 Communication networks
 * Historical perspective
 * From telephony to the Internet
 * The Web and Wikis
 * 1.2 Social networks
 * Online communities
 * Traditional social networks
 * 1.3 Networks everywhere
 * 1.4 Organization of this book


 * 2 Foundations
 * 2.1 Formalities
 * Graphs and vertex degrees
 * Degree sequence
 * Subgraphs and line graphs
 * 2.2 Graph representations
 * Data structures
 * Graph isomorphism
 * 2.3 Connectivity
 * 2.4 Drawing graphs
 * Graph embeddings
 * Planar graphs


 * 3 Extensions
 * 3.1 Directed graphs
 * Basics of directed graphs
 * Connectivity for directed graphs
 * 3.2 Weighted graphs
 * 3.3 Colorings
 * Edge colorings
 * Vertex colorings


 * 4 Network traversal
 * 4.1 Euler tours
 * Constructing an Euler tour
 * The Chinese postman problem
 * 4.2 Hamilton cycles
 * Properties of Hamiltonian graphs
 * Finding a Hamilton cycle
 * Optimal Hamilton cycles


 * 5 Trees
 * 5.1 Background
 * Trees in transportation networks
 * Trees as data structures
 * 5.2 Fundamentals
 * 5.3 Spanning trees
 * 5.4 Routing in communication networks
 * Dijkstra's algorithm
 * The Bellman-Ford algorithm
 * A note on algorithmic performance


 * 6 Network analysis
 * 6.1 Vertex degrees
 * Degree distribution
 * Degree correlations
 * 6.2 Distance statistics
 * 6.3 Clustering coefficient
 * Some effects of clustering
 * Local view
 * Global view
 * 6.4 Centrality


 * 7 Random networks
 * 7.1 Introduction
 * 7.2 Classical random networks
 * Degree distribution
 * Other metrics for random graphs
 * 7.3 Small worlds
 * 7.4 Scale-free networks
 * Fundamentals
 * Properties of scale-free networks
 * Related networks


 * 8 Modern computer networks
 * 8.1 The Internet
 * Computer networks
 * Measuring the topology of the Internet
 * 8.2 Peer-to-peer overlay networks
 * Structured overlay networks
 * Random overlay networks
 * 8.3 The World Wide Web
 * The organization of the Web
 * Measuring the topology of the Web


 * 9 Social networks
 * 9.1 Social network analysis: introduction
 * Examples
 * Historical background
 * Sociograms in practice: a teacher's aid
 * 9.2 Some basic concepts
 * Centrality and prestige
 * Structural balance
 * Cohesive subgroups
 * Affiliation networks
 * 9.3 Equivalence
 * Structural equivalence
 * Automorphic equivalence
 * Regular equivalence


 * Conclusions
 * Mathematical notations
 * Index
 * Bibliography