Analyzing the Temporal Exclusivity of Violent and Property Crime: A Circular Statistical Approach Based on Complex Vector Space

The current study examines the temporal exclusivity of crime across urban space. Specifically, we look at whether the temporal structure of crime differs between weekdays and weekends and map how these spatiotemporal synchronizations diverge between violent and property crime in New York City Crime incident hours were transformed into unit vectors on a circular plane using an aoristic allocation framework to handle temporal uncertainty. The Mean Resultant Length was calculated to measure the degree of temporal exclusivity at the block group level. To distinguish systematic diurnal rhythms from ambient stochastic noise while accounting for multiple comparison inflation, we implemented the Rayleigh test of uniformity. Violent crime exhibits stronger temporal concentration within individual locations but collapses to a relatively small number of statistically significant hotspots under stringent multiple-comparison corrections. This pattern likely reflects the combination of lower incident frequency and limited statistical power at the block group level. In contrast, property crime displays a more spatially robust pattern of temporal synchronization. Although its hourly concentration is generally less pronounced within individual locations, the substantially larger number of incidents produces stable and statistically reliable temporal rhythms across the city. The findings suggest that the temporal structure of crime is shaped by routine activity patterns that vary across the weekly cycle. By introducing a circular statistical framework to measure the temporal concentration of crime, this study highlights the importance of integrating temporal dynamics into research on crime and place.