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.

Provides a comprehensive review of this interdisciplinary field Illustrates how graph theory and statistical physics can help solving practical problems Contains many examples of real-world applications from transportation networks to the brain

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.

Résumé
"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)

Contenu
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.- Families of Models of Spatial Networks.- 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.