In this article, we develop a mathematical framework to model crime and crime concentrations on a city road network. The model proposed is an advancement to similar frameworks inspired by a model introduced by Short et al. (2008). A significant modification introduced in our model is the use of spectral graph theory to represent the road network and to simulate diffusion throughout the network. The techniques discussed are tested in a simulation model of crime applied to the city of Vancouver, BC, Canada. The simulations presented are based off of empirical data of crime in Vancouver along with its street network. Results of the simulations present crime patterns that are consistent with crime patterns observed in the city.
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