Robustness of urban bus traffic networks: A ‘load points’ analysis

The urban bus traffic network is one of the important instance in complex network researches. The robustness of public traffic networks is not only related to the efficiency and capacity of people movement, but also the critical aspects in future urban regulation and design. Traditionally, researches pay more attention to the influence of high-degree vertices (degree of a vertex is the number of other vertices linked to it) to network robustness, however, the degree cannot reflect comprehensive properties of complex networks. Here, we adopted a `load points´ analysis from cellular metabolic network researches to explore four real bus traffic networkes in China. Load point analysis emphasizes the role of the global network structure in a traffic system, rather than its local connectivity, plays in the transportation paths. Additionally, we use the degree and load of vertices to rank the stops in the bus traffic network, and perform attacks on the networks according to the ranks. We use the diameter of the network to measure the damage of the network. The result shows 1) there are no obvious relationship between the degree and the load of a vertex in the bus traffic network; 2) a few low-degree but high-load vertices are critical to maintain the robustness of the bus traffic network. Our works have both practical value for urban public traffic management and theoretical values for the development of interdiscipline science.