Role of spatial embedding and planarity in shaping the topology of the Street Networks

Abstract: The topology of city street networks (SNs) is constrained by spatial embedding, requiring non-crossing links and preventing random node placement or overlap. Here, we analyzed SNs of $33$ Indian cities to explore how the spatial embedding and the planarity jointly shape their topology. Overall, we found that all the studied SNs have small-world properties with higher clustering and efficiency. The efficiency of the empirical networks is even higher than that of the corresponding degree of preserved random networks. This increased efficiency can be explained by Dijkstra's path-length distribution, which closely fits a right-skewed normal or log-normal distribution. Moreover, we observed that the connectivity of the streets is length-dependent: the smaller streets connect preferably to the smaller streets, while longer streets tend to connect with the longer counterparts. This length-dependent connectivity is more profound in the empirical SNs than in the corresponding degree preserved random and random planar networks. However, planar networks maintaining the empirical spatial coordinates replicate the connectivity behavior of empirical SNs, highlighting the influence of spatial embedding. Moreover, the robustness of the cities in terms of resilience to random errors and targeted attacks is independent of the SN's size, indicating other factors, such as geographical constraints, substantially influence network stability.