Barthelemy M. Spatial Networks. A Complete Introduction...2022

Textbook in PDF format

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 reference on this topic for a wide range of students and professional researchers.
Characterization
From Complex to Spatial Networks
Planar Graphs
Directed and Mixed Graphs
Simple Measures
Betweenness Centrality
The Shape of Shortest Paths
Simplicity and Entropy
Large-Scale Tools
Typology of Planar Graphs .
Measuring the Time Evolution of Spatial Networks
Models
Spatial Generalizations of Random Graphs
Spatial Small-Worlds
Growing Spatial Networks .
Tessellations of the Plane
Proximity Graphs
Excluded Volume Graphs
Loops and Branches
Optimal Networks
Optimal Transportation Networks and Network Design
Greedy Models
tary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations