中国国内航空网络的分形特征研究

doi:10.3969/j.issn.1007-7375.2022.05.014

工业工程 ›› 2022, Vol. 25 ›› Issue (5): 113-119.doi: 10.3969/j.issn.1007-7375.2022.05.014

中国国内航空网络的分形特征研究

文军, 罗心雨, 钟佳轩, 徐志航

中国民用航空飞行学院机场工程与运输管理学院，四川广汉 618307

收稿日期:2021-05-10 发布日期:2022-10-20
作者简介:文军(1968—)，男，四川省人，教授，博士，主要研究方向为航空运输规划与管理
基金资助:
国家自然科学基金资助项目(61179074)

A Study of Fractal Features of Chinese Domestic Airline Network

WEN Jun, LUO Xinyu, ZHONG Jiaxuan, XU Zhihang

School of Airport Engineering and Transportation Management, Civil Aviation Flight University of China, Guanghan 618307, China

Received:2021-05-10 Published:2022-10-20
Supported by:
This work was supported by National Natural Science Foundation of China (No. 61179074).

摘要/Abstract

摘要： 为进一步探索中国航空网络拓扑结构的复杂性，以2015和2019年夏秋航季国内航班正班计划数据为例，以分形理论为基础，对中国航空网络分形特征进行实证分析。研究表明，中国航空网络具有较高的聚类系数和较短的平均路径长度，且度服从幂律分布，其具有小世界特征和无标度特征。度度相关性表现为负相关，网络为异配的。盒子尺寸l_B与最小盒子数N_B在双对数图中线性关系显著，表明中国航空网络在结构上具有自相似功能模块，具有分形特征。与2015年网络结构比较，2019年网络的平均最短路径和聚类系数均下降，而节点数和节点平均度增大,无权盒维数由2015年的5.065增长到5.079，加权盒维数从2.164增长到2.262，中国航空网络的分形结构随时间推移逐步演进，网络整体结构在趋好。

关键词: 中国航空网络, 复杂网络, 拓扑特性, 盒维数, 分形特征

Abstract: To further explore the complexity of Chinese airline network topology, based on the schedule data of domestic flights in the summer and autumn seasons of 2015 and 2019, an empirical analysis of the fractal characteristics of Chinese airline network is conducted by using the fractal theory. The research shows that: Chinese airline network has shorter average path length and clustering coefficient, and follows power-law distribution, having the characteristics of small world and scale-free feature. Degree correlation shows negative correlation and the network is heterotopic. The linear relationship between the box size l_B and the minimum box number N_B is significant in the log-log graph, which indicates that Chinese airline network has self-similar functional modules in structure, and it has fractal characteristics. Compared with network structure in 2015, in 2019 the average Chinese airline network shortest path and cluster coefficient decreased, and the number of nodes, the average degree of node, the dimension of no weight box increased from 5.065 in 2015 to 5.079, the weighted box dimension increased from 2.164 to 2.262, and as the fractal structure of Chinese airline network evolved over time, the overall structure of the network was getting better.

Key words: Chinese airline network, complex network, topological characteristics, box dimension, fractal characteristics

中图分类号:

F560

文军, 罗心雨, 钟佳轩, 徐志航. 中国国内航空网络的分形特征研究[J]. 工业工程, 2022, 25(5): 113-119.

WEN Jun, LUO Xinyu, ZHONG Jiaxuan, XU Zhihang. A Study of Fractal Features of Chinese Domestic Airline Network[J]. Industrial Engineering Journal, 2022, 25(5): 113-119.

参考文献

[1] SONG C, HAVLIN S, MAKSE H A. Self-similarity of complex networks[J]. Nature, 2005, 433(7024): 392-395
[2] 张明君. 分形理论在复杂网络研究中的应用[D]. 青岛: 青岛大学, 2008.
ZHANG Mingjun. Application of fractal theory in complex network research[D]. Qingdao: Qingdao University, 2008.
[3] GOU L, WEI B, SADIQ R, et al. Topological vulnerability evaluation model based on fractal dimension of complex networks [J/OL]. Plos One, 2016, 11(1): (2016-01-11). https://doi.org/10.137./journal.pone.0146896.
[4] 牟建红, 黄格, 吕欣. 中国航空网络时序特征分析[J]. 电子科技大学学报, 2018, 47(3): 462-468
MOU Jianhong, HUANG Ge, LYU Xin. Analysis of the temporal characteristics of Chinese aviation network[J]. Journal of University of Electronic Science and Technology of China, 2018, 47(3): 462-468
[5] 杨丽, 苟晓冬. 中国航空货运网络结构分析[J]. 西北师范大学学报(自然科学版), 2019, 55(4): 30-36
YANG Li, GOU Xiaodong. Analysis on China's air cargo network structure[J]. Journal of Northwest Normal University (Natural Science), 2019, 55(4): 30-36
[6] 王兴隆, 朱丽纳, 石宗北. 多层航线聚合网络建模及相关性分析[J]. 科学技术与工程, 2020, 20(3): 1243-1249
WANG Xinglong, ZHU Lina, SHI Zongbei. Multi-layer route aggregation network modeling and correlation analysis[J]. Science Technology and Engineering, 2020, 20(3): 1243-1249
[7] SONG C, HAVLIN S, MAKSE H A. Origins of fractality in the growth of complex networks[J]. Nature Physics, 2006, 2(4): 275-281
[8] SONG C, CALLOS L K, HAVLIN S, et al. How to calculate the fractal dimension of a complex network: The box covering algorithm[J]. Journal of Statistical Mechanics Theory and Experiment, 2007(3): 297-316
[9] 姚灿中, 杨建梅. 复杂网络分形的盒维数改进算法[J]. 计算机工程与应用, 2010, 46(8): 5-7
YAO Canzhong, YANG Jianmei. Improved box dimension calculation algorithm for fractality of complex networks[J]. Computer Engineering and Applications, 2010, 46(8): 5-7
[10] WEI D, LIU Q, ZHANG H, et al. Box-covering algorithm for fractal dimension of weighted networks[J]. Scientific Reports, 2013, 3(1): 1799-1807
[11] 孙梦丹. 基于复杂网络的中国航空网络研究[D]. 青岛: 青岛理工大学, 2017.
SUN Mengdan. Empirical Study of Chinese airline network based on complex network theory[D]. Qingdao: Qingdao University of Technology, 2017.
[12] PASTOR-SATORRAS R , VESPIGNANI A. Epidemic spreading in scale-free networks[J]. Physical Review Letters, 2001, 86(14): 3200-3203
[13] VÁZQUEZ A, PASTOR-SATORRAS E, VESPIGNANI A. Large-scale topological and dynamical properties of the Internet [J/OL]. Physical Review E, 2002, 65: (2002-06-28). https://doi.org/10.1103/PhysRevE.65.066130.
[14] NEWMAN M E J. Mixing patterns in networks [J/OL]. Physical Review E, 2003, 67: (2003-02-27). https://doi.org/10.1103/PhysRevE.67.026126.
[15] 陈志鹏, 谢宁, 王承民, 等. 基于分形机理的复杂电力网络脆弱性评估及鲁棒性提升策略研究[J]. 电网技术, 2021, 45(2): 657-665
CHEN Zhipeng, XIE Ning, WANG Chengmin, et al. Vulnerability evaluation and robustness improvement strategy of complex power network based on fractal mechanism[J]. Power System Technology, 2021, 45(2): 657-665

中国国内航空网络的分形特征研究

A Study of Fractal Features of Chinese Domestic Airline Network

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

[1]	张富强1，江平宇2. 复杂网络理论在离散车间生产过程的应用研究综述[J]. 工业工程, 2016, 19(6): 1-8.
[2]	刘向荣1，杨建梅1，孙红英2，谢伟聪1. 基于符号动力学的中国工业产品价格传导复杂网络分析[J]. 工业工程, 2013, 16(4): 49-55.