基于复杂网络理论的北京公交网络拓扑性质分析

Analysis on topological properties of Beijing urban public transit based on complex network theory

为分析公交复杂网络的拓扑性质,本文以北京市为例,选取截止到2010年7月的北京全市(14区、2县)的1165条公交线路和9618个公交站点为样本数据,运用复杂网络理论构建起基于邻接站点的有向加权复杂网络模型.该方法以公交站点作为节点,相邻站点之间的公交线路作为边,使得网络既具有复杂网络的拓扑性质同时节点(站点)又具有明确的地理坐标.对网络中节点度、点强度、强度分布、平均最短路径、聚类系数等性质的分析显示,公交复杂网络的度和点强度分布极为不均,网络中前5%和前10%节点的累计强度分布分别达到22.43%和43.02%;点强度与排列序数、累积强度分布都服从幂律分布,具有无标度和小世界的网络特点,少数关键节点在网络中发挥着重要的连接作用.为分析复杂网络中的关键节点,本文通过承载压力分析和基于"掠夺"的区域中心节点提取两种方法,得到了公交复杂网络中两类不同表现的关键节点.这些规律也为优化城市公交网络及交通规划发展提供了新的参考建议.

To analyze the topological properties of Beijing public transport network, until July 2010, we have collected 1165 bus lines and 9618 bus stops of Beijing City （14 districts and 2 counties） as the sample data to build up a directed and weighted complex network model based on neighboring stops by applying the complex network theory. In this model, bus stops are considered as nodes of the complex network, while bus lines connecting two neighboring stops as edges. Consequently, the network has the topological properties of a complex network and meanwhile the nodes （bus stops） have clear geographic coordinates. The complexity of Beijing public transport is then verified through analyzing the topological properties of node degree, node strength, strength distribution, average shortest path, clustering coefficient in the complex network. We find that the distributions of node degrees and node strengths are extremely uneven and the cumulative strength distributions of the top 5% and 10% nodes reach 22.43% and 43.02% respectively. The results also show that the node strength, ordinal number and cumulative strength distribution of the nodes all follow the power-law distribution, showing the network characteristics of scale-free and small world. Some ＂key nodes＂ play an important role in network connection. We find two kinds of ＂key nodes＂ by using high carrying pressure node analysis and extract regional central analysis. These rules provide new references for optimizing the urban transport network, managing traffic congestion and planning and developing the traffic.