Measuring road network topology vulnerability by Ricci curvature

Describing the basic properties of road network systems, such as their robustness, vulnerability, and reliability, has been a very important research topic in the field of urban transportation. Current research mainly uses several statistical indicators of complex networks to analyze the road network systems. However, these methods are essentially node-based. These node-based methods pay more attention to the number of connections between nodes, and lack of consideration for interactions, leading to the well-known node paradox problem, and their ability of characterizing the local and intrinsic properties of a network is weak. From the perspective of network intrinsic geometry, we propose a method for measuring road network vulnerability using a discrete Ricci curvature, which can identify the key sections of a road network and indicate its fragile elements. The results show that our method performs better than complex network statistics on measuring the vulnerability of a road network. Additionally, it can characterize the evolution of the road network vulnerability among different periods of time in the same city through our method. Finally, we compare our method with the previous method of centrality and show the different between them. This research provides a new perspective on a geometry to analyze the vulnerability of a road network and describes the inherent nature of the vulnerability of a road system from a new perspective. It also contributes to enriching the analytical methods of complex road networks.