Efficiency in the evolution of metro networks

Metro systems extended rapidly in China, especially in the last decade, developing over a half-century. This work explores the dynamical evolution of the structural efficiency of metro systems interpreted as complex networks for 14 large cities in mainland China. Based on the empirical observations, we find that the global efficiencies scale with the number of stations and counter-intuitively decreases as the metro networks expand, which shows a long-tail characteristic. The evolution of metro networks is, in essence, the improvement of the relative ratio of average nodal efficiency in the core compared to global efficiency. These relationships are in good agreement with the temporal structure of metro networks. Besides, we find that the metro stations with the higher efficiencies are those surrounding the urban center, and most of them dwell within the core and gradually expand the branches in space. Our findings suggest that the evolution properties of metro systems influenced by numerous geographical, historical, and social activities suggest that underlying, universal mechanisms are at play during their evolution in the spatial-temporal dimension.