A Study of Fractal Features of Chinese Domestic Airline Network

doi:10.3969/j.issn.1007-7375.2022.05.014

Abstract

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

CLC Number:

F560

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.

References

[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