Metros (heavy rail transit systems) are integral parts of urban transportation systems. Failures in their operations can have serious impacts on urban mobility, and measuring their robustness is therefore critical. Moreover, as physical networks, metros can be viewed as topological entities, and as such they possess measurable network properties. In this article, by using network science and graph theory, we investigate ten theoretical and four numerical robustness metrics and their performance in quantifying the robustness of 33 metro networks under random failures or targeted attacks. We find that the ten theoretical metrics capture two distinct aspects of robustness of metro networks. First, several metrics place an emphasis on alternative paths. Second, other metrics place an emphasis on the length of the paths. To account for all aspects, we standardize all ten indicators and plot them on radar diagrams to assess the overall robustness for metro networks. Overall, we find that Tokyo and Rome are the most robust networks. Rome benefits from short transferring and Tokyo has a significant number of transfer stations, both in the city center and in the peripheral area of the city, promoting both a higher number of alternative paths and overall relatively short path-lengths.

In this paper we take one of the cutting edge algorithms for computing the all-terminal reliability and the k-terminal reliability of a network and use it to compute the reliability of a real life gas distribution network in the Netherlands. To do this we estimate network properties using industry knowledge and combine several different techniques to make the problem computable. This is the first time known to us that these techniques have been applied to a large, in this case over 20000 nodes, real life network. Besides this, we show the versatility of this pathwidth-based dynamic programming algorithm by suggesting some powerful but simple modifications and argue that this network is representative for other distribution networks.