Scale-free Networks

A variety of different social, natural, and technological systems can be described by the same mathematical framework. This holds from the Internet to food webs and to boards of company directors. In all these situations a graph of the elements of the system and their interconnections displays a universal feature. There are only few elements with many connections, and many elements with few connections. This book presents the experimental evidence of these 'scale-free networks' and provides students and researchers with a corpus of theoretical results and algorithms to analyse and understand these features. The content of this book and the exposition makes it a clear textbook for beginners, and a reference book for the experts.1. Introduction to Graphs ; 2. Graph structure: Communities ; 3. Scale-invariance ; 4. The Origin of power law functions ; 5. Graph Generating Models ; 6. Networks in the cell ; 7. Ecological networks ; 8. Geophysical networks ; 9. Technological networks: Internet and WWW ; 10. Collaborative Relational and Cognitive Networks ; 11. Financial networks ; 1. Introduction to Graphs ; 2. Graph structure: Communities ; 3. Scale-invariance ; 4. The Origin of power law functions ; 5. Graph Generating Models ; 6. Networks in the cell ; 7. Ecological networks ; 8. Geophysical networks ; 9. Technological networks: Internet and WWW ; 10. Collaborative Relational and Cognitive Networks ; 11. Financial networks