Integrating bipartite network modelling and overlapping community detection: A new method to evaluate transit line coordination

This paper introduces a novel approach, integrating bipartite network modelling and overlapping community detection, to evaluate the coordination of transit lines in public transport systems. The bipartite networks capture the affiliation relationship between transit lines and stations, considering both transfer distance and service frequency. We adapt the BiEgoNet-based and BiClique-based algorithms for overlapping community detection in the bipartite transport network, and employ four indices to evaluate the quality of bipartite community partition from the perspective of community connectedness (extended modularity, community partition density and route diversity) and independence (community partition independence). Additionally, we propose two metrics, coordination scale and variance, to analyse transit line coordination. The former metric measures the overall ability of a transit line to coordinate, and the later metric quantify the variance of the coordination property along a transit line. The proposed methods are tested in the public transport system of Urumqi, China, and the results demonstrate that these metrics effectively reveal the ability and inclination of transit lines to interact, based on their distributions, lengths, and station numbers. This research contributes to the understanding and assessment of redundancy and resilience in public transport systems through innovative bipartite network modelling and community detection.