Spatial dependency of bus-line distribution based on bipartite network: A case study of Beijing city

As a subnet derived from and supplied by urban road network, public transport network (PTN) owes its maximum development to the development level of urban road network. The structural defects of PTN often make itself the culprit of urban traffic congestion. Traditional research on spatial distribution of PTN tends to regard PTN as an independent mode of transportation, but overlooks the endogenous effect of urban road network's morphology and structure. Based on the idea of binary network, this paper discusses the local and global spatial dependency of Beijing bus- line distribution by constructing the space correlation matrix between bus line and city road and introducing dependency measures from 1- mode network. This endeavor also divides the dependence space of Beijing bus lines by community detection with the help of the software named Ucinet 6. We find out that in terms of local dependence, the layout of bus lines is highly dependent on a few city trunk roads and expressways connecting downtown areas and suburbs, so its spatial dependence shows a corridor diffusion pattern of core- periphery, which takes the downtown as the core and the rapid suburban corridors as the channel. In terms of global dependence, the unbalanced distribution structure of bus lines seems more fragile and is greatly influenced by the city road traffic conditions. Meanwhile, the downtown area bounded by the Fourth Ring Road becomes the core space of bus- line dependence. In terms of space division, the layout of Beijing bus lines presents good correspondence to the city districts. To exemplify this, Chaoyang District, Haidian District and the area within the Third Ring Road have the densest bus- line distributions.