Identification of patterns for space-time event networks

Abstract

This paper provides new tools for analyzing spatio-temporal event networks. We build time series of directed event networks for a set of spatial distances, and based on scan-statistics, the spatial distance that generates the strongest change of event network connections is chosen. In addition, we propose an empirical random network event generator to detect significant motifs throughout time. This generator preserves the spatial configuration but randomizes the order of the occurrence of events. To prevent the large number of links from masking the count of motifs, we propose using standardized counts of motifs at each time slot. Our methodology is able to detect interaction radius in space, build time series of networks, and describe changes in its topology over time, by means of identification of different types of motifs that allows for the understanding of the spatio-temporal dynamics of the phenomena. We illustrate our methodology by analyzing thefts occurred in Medellín (Colombia) between the years 2003 and 2015.