Tracking of a dynamic graph using a signal theory approach : application to the study of a bike sharing system

Dynamic graphs are useful objects to describe a network which evolves over time. We propose a signal theory approach to analyze them which consists of transforming the graph at each time step into a collection of signals and analyze these signals using spectral decomposition. An inverse transformation is also proposed and makes it possible to reduce the dimension of the graph and select the most significant edges. The method is applied on a real dynamic graph based on data about the bike sharing system Velo'v in Lyon. The analysis of signals representing the graph highlights the weekly cycle of rentals and the inverse transformation enables us to obtain sparser graphs.