Title: Natural Scales in Geographical Patterns,
Abstract: Human mobility is known to be distributed across several orders of magnitude
of physical distances , which makes it generally difficult to endogenously find
or define typical and meaningful scales. Relevant analyses, from movements to
geographical partitions, seem to be relative to some ad-hoc scale, or no scale
at all. Relying on geotagged data collected from photo-sharing social media, we
apply community detection to movement networks constrained by increasing
percentiles of the distance distribution. Using a simple parameter-free
discontinuity detection algorithm, we discover clear phase transitions in the
community partition space. The detection of these phases constitutes the first
objective method of characterising endogenous, natural scales of human
movement. Our study covers nine regions, ranging from cities to countries of
various sizes and a transnational area. For all regions, the number of natural
scales is remarkably low (2 or 3). Further, our results hint at scale-related
behaviours rather than scale-related users. The partitions of the natural
scales allow us to draw discrete multi-scale geographical boundaries,
potentially capable of providing key insights in fields such as epidemiology or
cultural contagion where the introduction of spatial boundaries is pivotal.