Название: Spatial Networks: A Complete Introduction: From Graph Theory and Statistical Physics to Real-World Applications
Автор: Marc Barthelemy
Издательство: Springer
Год: 2022
Страниц: 443
Язык: английский
Формат: pdf (true)
Размер: 15.4 MB

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, we will discuss different aspects of spatial networks, focusing essentially on the characterization of their structure and on their modeling. Each chapter is as much as possible self-contained, and for the sake of clarity and readability, we tried to be as modular as possible in order to allow the reader interested in just one specific model or tool to focus essentially on the corresponding chapter.

In the Chaps. 1–4 about characterization, I go over classical notions such as planar graphs or digraphs but I always try to present a particular point of view by insisting on aspects that are usually put aside by many authors. I also try to add an empirical grain of salt in all chapters. In this way, I can illustrate complex notions in a simple, concrete way and show that they are actually useful.

Shortest paths are crucial for understanding the structure of networks, and in particular, the betweenness centrality discussed in Chap. 5 is a simple tool that contains a lot of information and reveals quite a lot about the structure of a graph. The shape of shortest paths discussed in Chap. 6 is also an important topic in relation with first passage percolation, a standard problem in statistical physics. In Chap. 7 I discuss other types of paths: the simples paths which try to avoid turns as much as possible, and show how they bring us information about the mesoscopic structure of large networks. The entropy counts the complexity of paths in these networks and is also discussed in this chapter. In Chap. 8, I will present various tools that allow to characterize the structure of spatial networks at a large scale.