Spatial Networks

This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks. The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology. This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and referenceon this topic for a wide range of students and professional researchers.

Auteur

Marc Barthelemy is a former student of the Ecole Normale Superieure of Paris. In 1992, He graduated at the University of Paris VI with a thesis in theoretical physics titled "Random walks in random media". After his thesis, he focused on disordered systems and their properties, and since 1992, he have held a permanent position at the CEA. Presently, Marc Barthelemy is a research director at the Institute of Theoretical Physics (IPhT) in Saclay and a member of the Center of Social Analysis and Mathematics (CAMS) at the Ecole des Hautes Etudes en Sciences Sociales (EHESS).

His research interests moved towards applications of statistical physics to complex systems, complex networks, theoretical epidemiology, and more recently on spatial networks. Focusing on both data analysis and modeling with the tools of statistical physics, Barthelemy is currently also working on various aspects of the emerging science of cities.

Contenu

0. Introduction
   I. Characterization
1. Planar graphs
2. Simple measures
3. Betweenness centrality
4. Simplicity and Entropy
5. The shape of shortest paths
6. Spatial dominance
7. Typology of spatial networks
8. Time evolution of spatial networks
   II. Models
9. Spatial random graphs
10. Tesselations of the plane
11. Random geometric graphs
12. beta-skeletons
13. Loops and branches
14. Optimal networks
15. Growing networks
16. Greedy models
17. Transitions in spatial networks
18. Multilayer networks
    III. Discussion and perspectives