重庆理工大学学报2025，Vol.39Issue(23)：227-235,9.DOI:10.3969/j.issn.1674-8425(z).2025.12.028
城市轨道交通网络多阶段演化特征分析
Analysis of multi-stage evolution characteristics of urban rail transit networks
摘要
Abstract
The transition of urban rail transit systems from simple"line-based"configurations to complex"network-based"structures not only enhances network effects and passenger attraction,but also achieves pronounced heterogeneity in network maturity,structural characteristics,and operational performance across cities.Previous studies tend to emphasize static topological attributes.Limited to a single city,they lack a unified,generalizable framework for classifying developmental stages across citites with different contexts.To bridge this gap,this paper proposes a data-driven analytical framework that identifies and characterizes the evolutionary stages of urban rail transit networks in China,providing a theoretical foundation for designing stage-specific planning and operational strategies. The topological networks for 39 Chinese cities are built by using data obtained from the Amap Open Platform and employing the Space L modelling approach.A comprehensive indicator system incorporating both subjective and objective metrics is built,covering key dimensions:network scale(the number of stations,lines,and operating mileage),topological structure,network diameter,average path length,clustering coefficient,and three centrality measures(average degree,betweenness,and closeness);and passenger attributes,represented by monthly per capita trip frequency derived from annual passenger volume and urban population data.To mitigate dimensionality issues and multicollinearity among indicators,Principal Component Analysis is employed for dimensionality reduction.The first two principal components are retained,accounting for 89.70％of the cumulative variance.The Gaussian Mixture Model(GMM)is applied for cluster analysis.Four clusters are identified as optimal based on the Calinski-Harabasz and Davies-Bouldin indices,confirming that GMM outperforms alternative methods such as K-means in capturing the underlying data structures. GMM clearly delineates the urban rail transit networks into four distinct developmental stages.The first stage,Initial Development,features small-scale systems such as those in Taiyuan and Urumqi,typically consisting of 1-3 lines,fewer than 30 stations,and an operating mileage below 30 km.In this stage,all topological metrics and passenger frequency remain at their minimal levels.The second stage,Expansion,includes cities like Hefei and Ningbo,where a basic network skeleton forms with 3-5 lines,approximately 81 stations,and a mileage reaching 200 km.This phase shows significant increases in network diameter and average path length,reflecting spatial expansion and growing complexity.The third stage,Networked Operation,represented by cities such as Suzhou and Xi'an,features extensive systems with 5-10 lines,100-200 stations,and a mileage ranging from 200-400 km.This stage exhibits peak values in network diameter and average path length,indicating maximum spatial span.Concurrently,declining centrality measures signal a transition from core structure toward a more balanced distribution of node importance.The fourth stage,Maturity and Enhancement,exemplified by Beijing,Shanghai,and Guangzhou,demonstrates large-scale networks with over 10 lines,200 stations,and 400 km of mileage.The developmental focus shifts decisively from spatial expansion to internal intensification and optimization,resulting in markedly shortened average path length.A salient feature of this stage is the notable leap in monthly per capita trip frequency,highlighting enhanced network utility and increased public reliance. Based on complex network theory and GMM clustering,this paper builds a multi-stage evolution model for urban rail transit networks.The four stages exhibit distinctive characteristics in scale,structure,and functionality,providing actionable insights for urban transportation planning.The findings indicate cities in the initial development stage should give priorities to form core corridors and expand the network skeleton.Those in the networked operation stage need to focus on structural optimization and enhanced operational resilience.For cities reaching maturity,emphasis should be given to service intensification and improvement of operational efficiency.This paper may provide some insights for decision-makers and planners into formulating dynamic strategies tailored to specific developmental stages of urban rail transit networks.关键词
城市轨道交通网络/网络演化/发展阶段/复杂网络指标/高斯混合模型Key words
urban rail transit network/network evolution/development stage/complex network index/GMM分类
交通工程引用本文复制引用
LI Qing,ZHU Zhenjun,ZHAO Yunpeng,ZHANG Xuhui,LIN Yishu..城市轨道交通网络多阶段演化特征分析[J].重庆理工大学学报,2025,39(23):227-235,9.基金项目
国家自然科学基金青年项目(52402385) （52402385）
江苏省研究生科研与实践创新计划项目(SJCX24_0405) （SJCX24_0405）
