From Complex to Spatial Networks

Abstract

The study of spatial networks – networks embedded in space – started essentially with quantitative geographers in the 60–70 s who studied the structure and the evolution of transportation systems. The interest for networks was revived by Watts and Strogatz who opened the way to a statistical physics type of analysis and modeling of large networks. This renewed interest, together with an always growing availability of data, led to many studies of networks and their structures. Most of these studies focused on the topological properties of networks, leaving aside their spatial properties. It is only recently that researchers realized the importance of geometry – as opposed to topology – for spatial networks. In this chapter, we first describe briefly the evolution of these fields and ideas about spatial networks. Most of these objects are planar and in the second part of this chapter, we give basic definitions and results for planar graphs.