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

Abstract

The topology of city street networks (SNs) is bounded by spatial embedding, which enforces non-crossing links and prohibits random node placement or overlap. This raises a fundamental question: how do such spatial constraints shape network topology? To address this, we analyze the SNs of 33 Indian cities. All studied networks exhibit small-world properties characterized by high clustering and efficiency. Notably, the efficiency of the empirical networks exceeds that of corresponding degree-preserved random networks. This elevated efficiency is attributed to the right-skewed distribution of Dijkstra’s path lengths, a pattern also observed in random planar networks. While the average Dijkstra path length scales with the mean street length, the overall distribution is more strongly influenced by geometric structure and planarity than by scaling alone. Furthermore, we observe a clear preference for length-based connectivity: shorter streets preferentially connect to other short streets and longer ones to longer counterparts, which is more pronounced in empirical SNs than in degree-preserved or random planar networks. However, planar networks, preserving the spatial coordinates of empirical networks, replicate this connectivity pattern, pointing to the role of spatial embedding. Finally, the resilience of the Indian SNs to edge-based random errors and targeted attacks remains independent of the SN’s size, indicating that other factors, such as geographical constraints, substantially influence network stability. Our findings provide insights into how spatial constraints shape the topology and function of urban street networks.