Evaluation of robustness in underground networks

Since the development of urban public mass transport in cities, transport infrastructures are a milestone for the economies of the cities and those of their respective regions. The construction of underground systems has seen impressive growth in many transport networks in the past few years, becoming the hinge of mobility in many of the principal cities of the world. Due to the latter and because of the possibility of disruptive events (natural disasters, random failures, and intentional attacks), many scholars and governments have worried about how robust the networks are. For this reason, in this paper we reviewed the robustness of networks by using graph theory tools to analyze and measure them through a new centrality index, called Sum of Weighted Distances Index (SWDI). The index measures the percentage of changes in traveled distances in the event that the node and all edges containing it are disrupted. To evaluate the robustness of a network, we compare the outcomes of SWDI at a standard working configuration and at a degraded one, modeled as a reduction of performance at a certain edge, edge by edge. SWDI is able to show at what edges and nodes of the network the degradation will have the highest impact. Summing up the normalized SWDI outcomes for all the nodes and edges, the final evaluation of the robustness of the network is obtained. Applications to the two case studies of Boston and Barcelona are developed, compared, and discussed, limited to their topology.