Urban retail location: Insights from percolation theory and spatial interaction modeling

Characterising road networks has been the focus of a large body of research due to it being the main driver of activities in an urban ecosystem and the structuring factor in the dynamics of the city. One of these activities, and one with the largest economical impact in a city, is retail dynamics and its evolution. Therefore, the mathematical modeling of the location of retail activities and of the emergence of clustering in retail centers has as well generated a large number of works. Despite these two interwoven components strongly depending on one another and their fundamental importance in understanding cities, little work has been done in order to compare their local and global properties. Here we compare the road network's hierarchical structure, unveiled through a percolation analysis of the network, with the retail location distribution defined by exploiting a gravity-based retail model. We interpret the great agreement in the city's organizations as it emerges from both methodologies as new evidence of the interdependence of these two crucial dimensions of a city's life.