Description
Book SynopsisThis 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 reference on this topic for a wide range of students and professional researchers.
Trade Review“This book, written by a statistical physicist, has the style of a survey rather than a mathematics textbook. It outlines numerous results (around 500 papers are cited) via descriptions of statistics and models and back-of-envelope calculations and simulation results together with real-world data examples. It is fairly technically undemanding, meaning mostly accessible to an advanced undergraduate mathematics student. … This book succeeds admirably in its stated ‘complete Introduction’ goal … .” (David J. Aldous, Mathematical Reviews, October, 2022)
Table of Contents0. 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
1. Spatial random graphs
2. Tesselations of the plane
3. Random geometric graphs
4. beta-skeletons
5. Loops and branches
6. Optimal networks
7. Growing networks
8. Greedy models
9. Transitions in spatial networks
10. Multilayer networks
III. Discussion and perspectives
