Statistics of Faces and Typology of Planar Graphs

Abstract

From a theoretical point of view, an important problem amounts to understand the structure of random planar graphs and eventually to propose a classification of these objects. In this chapter, we will discuss three different approaches. In the first one, we discuss the statistics of the area and shape of faces, and we apply this to street networks. The possibility of defining a distance between two graphs allows to propose a first simple typology of planar graphs and in particular of street networks. In a second approach, a decimation process is used in order to constructing an approximate mapping from a (weighted) planar graph to a tree. Finally, in a third part, we discuss a more mathematical approach based on an exact bijection between a planar graph and a tree.