  Pervasive infrastructures, such as cell phone networks, enable to capture
large amounts of human behavioral data but also provide information about the
structure of cities and their dynamical properties. In this article, we focus
on these last aspects by studying phone data recorded during 55 days in 31
Spanish metropolitan areas. We first define an urban dilatation index which
measures how the average distance between individuals evolves during the day,
allowing us to highlight different types of city structure. We then focus on
hotspots, the most crowded places in the city. We propose a parameter free
method to detect them and to test the robustness of our results. The number of
these hotspots scales sublinearly with the population size, a result in
agreement with previous theoretical arguments and measures on employment
datasets. We study the lifetime of these hotspots and show in particular that
the hierarchy of permanent ones, which constitute the "heart" of the city, is
very stable whatever the size of the city. The spatial structure of these
hotspots is also of interest and allows us to distinguish different categories
of cities, from monocentric and "segregated" where the spatial distribution is
very dependent on land use, to polycentric where the spatial mixing between
land uses is much more important. These results point towards the possibility
of a new, quantitative classification of cities using high resolution
spatio-temporal data.
