Empirical study on a directed and weighted bus transport network in China

• The difference between uplink and downlink for BTN-H is analyzed.
• The directed-space P representation model for BTNs is proposed.
• The four empirical distributions of BTN-H are presented following the exponential law.
• The rich-club phenomenon is demonstrated in BTN-H.

Bus transport networks are directed complex networks that consist of routes, stations, and passenger flow. In this study, the concept of duplication factor is introduced to analyze the differences between uplinks and downlinks for the bus transport network of Harbin (BTN-H). Further, a new representation model for BTNs is proposed, named as directed-space P. Two empirical characteristics of BTN-H are reported in this paper. First, the cumulative distributions of weighted degree, degree, number of routes that connect to each station, and node weight (peak-hour trips at a station) uniformly follow the exponential law. Meanwhile, the node weight shows positive correlations with the corresponding weighted degree, degree, and number of routes that connect to a station. Second, a new richness parameter of a node is explored by its node weight and the connectivity, weighted connectivity, average shortest path length and efficiency between rich nodes can be fitted by composite exponential functions to demonstrate the rich-club phenomenon.