1Institut de Physique Théorique, CEA-CNRS (URA 2306), F-91191, Gif-sur-Yvette, France.
2Gégraphie-Cités, CNRS-Paris 1-Paris 7 (UMR 8504), 13 rue du four, FR-75006 Paris, France.
3Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain.
4Nommon Solutions and Technologies, calle Cañas 8, 28043 Madrid, Spain.
5Telefónica Research, 28050 Madrid, Spain.
6Centre d'Analyse et de Mathématique Sociales, EHESS-CNRS (UMR 8557), 190-198 avenue de France, FR-75013 Paris, France.
|The extraction of a clear and simple footprint of the structure of large, weighted and directed networks is a general problem that has relevance for many applications. An important example is seen in origin-destination matrices, which contain the complete information on commuting flows, but are difficult to analyze and compare. We propose here a versatile method, which extracts a coarse-grained signature of mobility networks, under the form of a 2x2 matrix that separates the flows into four categories. We apply this method to origin-destination matrices extracted from mobile phone data recorded in 31 Spanish cities. We show that these cities essentially differ by their proportion of two types of flows: integrated (between residential and employment hotspots) and random flows, whose importance increases with city size. Finally, the method allows the determination of categories of networks, and in the mobility case, the classification of cities according to their commuting structure.|