Analysis of the dynamic relationship between traffic accident events and road network topology based on connectivity and graph analytics offers a new approach to identifying, ranking and profiling traffic accident high risk-locations at different levels of space and time granularities. Previous studies on traffic accident hot spots have mostly adopted spatial statistics and Geographic Information Systems (GIS) where spatial point patterns are discovered based only on spatial dependence with no recognition of the temporal dependence of the events. A limitation arises from the fact that the results are either under or over-estimated because of the temporal aggregation of the events to an absolute time point. Furthermore, the existing methods apart from the Network Kernel Density Estimation (NETKDE), consider traffic accident events as events randomly on a 2-D geographic space. However, traffic accident events are network constrained events that happens majorly on the road network space. Therefore, in this paper, we adopt the connectivity of graph on a network space approach that identifies accident high risk-locations based on space-time-varying connectivity between traffic accident events and the road network geometry. A simple but extensible traffic accident space time-varying graph (STVG) model is developed and implemented for this study. Traffic accident high risk-locations are identified and ranked in space and time using time-dependent degree centrality and PageRank centrality graph metrics respectively through time-incremental graph queries. This study offers urban traffic accident analysts with a new and efficient approach to identify, rank and profile accident-prone areas in space and time at different scales.