  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 are more concerned with the number of connections between nodes, and
lack of consideration for interactions. So, this leads 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, this paper proposes 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 article 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.
