Investigating transport network vulnerability by capacity weighted spectral analysis

- Capacity weighted spectral partitioning is used to find capacity bottlenecks in transport networks.
- The significance of the second smallest eigen value and corresponding vector of the graph Laplacian (normalized or otherwise) is explained.
- An improvement to Cheeger's inequality is derived.
- Results are presented for a 5-node illustrative example, the Sioux Falls road network and the Gifu Prefecture road network.
- A new method is offered for transport planners and network designers to identify potential transport network bottlenecks in the absence of demand information.

Transport networks operating at or near capacity are vulnerable to disruptions, so flow bottlenecks are potent sources of vulnerability. This paper presents an efficient method for finding transport network cuts, which may constitute such bottlenecks. Methods for assessing network vulnerability found in the literature require origin-destination demands and path assignment. However, in transport network planning and design, demand information is often missing, out of date, partial or inaccurate. Capacity weighted spectral partitioning is proposed to identify potential flow bottlenecks in the network, without reference to demand information or path assignments. This method identifies the network cut with least capacity, taking into account the relative sizes of the sub-networks either side of the cut. Spectral analysis has the added advantage of tractability, even for large networks, as shown by numerical examples for a five-node illustrative example, the Sioux Falls road network and the Gifu Prefecture road network.