Selection of a spatial hypothesis in geographic profiling using graph theory

Geographic profiling is based on the spatial hypothesis of a distance decay effect around the offender’s anchor point and can be very useful for delineating prior search areas for individual investigations such as DNA testing. However, this spatial hypothesis fails to model a significant part of Belgian serial sexual offenders. In previous study, a complementary hypothesis, the minimisation of the variance (MOV) for the distances between the offender’s anchor point and the crime site, exploiting recent literature observation, is proposed to model unexplained behaviours. A systematic comparison of the distance decay and the MOV hypotheses show that their overall capacities to provide an effective geoprofile are similar, but their performances may differ, depending on the geometric pattern of crimes. Here, we use graph theory to describe the favourable patterns for the MOV, in order to select which spatial hypothesis is best suited for a new investigation. While star graphs represent patterns for which both hypotheses could be validated, wheels with preferred directions are only explained by the MOV hypothesis. Real patterns on the road network are a-posteriori evaluated thanks to the generation of the shortest path between the best solution of the MOV and all the crime locations thanks to the Dijkstra algorithm.