Centrality maps and the analysis of city street networks

Firstly introduced in social science, the notion of centrality has spread to the whole complex network science. A centrality is a measure that quantifies whether an element of a network is well served or not, easy to reach, necessary to cross. This article focuses on cities' street network (seen as a communication network). We redefine two classical centralities (the closeness and the straightness) and introduce the notion of simplest centrality. To this we introduce a mathematical framework which allows considering a city as a geometrical continuum rather than a plain topological graph. The color plotting of the various centralities permits a visual analysis of the city and to diagnose local malfunctionings. The relevance of our framework and centralities is discussed from visual analysis of French towns and from computational complexity.