{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T07:05:00Z","timestamp":1766732700078,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T00:00:00Z","timestamp":1649635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As airspace congestion becomes more and more serious, it not only affects the efficiency and quality of aviation activities, but also poses a greater safety hazard. For in-depth exploration of the airspace network, a new airspace association network that differs from the traditional aviation approach of organizing the airspace into a network of sectors based on aircraft traffic flow is proposed. By judging the relationship between the size and location of the airspace and other properties, the establishment of an association network provides new ideas for airspace conflict detection and other aerial tasks. The three key factors of airspace use conflict were extracted and quantified, then the Analytic Hierarchy Process (AHP) was used to assign weights to basic symmetric operators corresponding to three factors to calculate the final airspace correction degree, which reveals the magnitude of correlation degree between the airspace caused by the combined action of the above three factors. Finally, an airspace association network model was established according to the association degree, using basic symmetric operators to explore the general symmetry and network characteristics in real-world airspace association networks, and the feature indices, such as degree, strength, average correlation, clustering coefficient, and structure information entropy of the network, are proposed. The results show that the nodes with higher node degree and node association strength are often key nodes in the network, and the areas with higher average association degree and clustering coefficient are often more prone to airspace conflicts. At the same time, it was also verified that the safety distance between airspace has the greatest impact on the characteristics of the airspace association network.<\/jats:p>","DOI":"10.3390\/sym14040790","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T22:48:45Z","timestamp":1649803725000},"page":"790","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Complex Network-Based Airspace Association Network Model and Its Characteristic Analysis"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7050-8630","authenticated-orcid":false,"given":"Ming","family":"Cai","sequence":"first","affiliation":[{"name":"Air Traffic Control and Navigation College, Air Force Engineering University, Xi\u2019an 710038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lujun","family":"Wan","sequence":"additional","affiliation":[{"name":"Air Traffic Control and Navigation College, Air Force Engineering University, Xi\u2019an 710038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"Zhong","sequence":"additional","affiliation":[{"name":"Information and Navigation College, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Equipment Management and UAV Engineering College, Air Force Engineering University, Xi\u2019an 710038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhizhou","family":"Gao","sequence":"additional","affiliation":[{"name":"Air Traffic Control and Navigation College, Air Force Engineering University, Xi\u2019an 710038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyu","family":"Xu","sequence":"additional","affiliation":[{"name":"Unit 95835 of the People's Liberation Army, Urumqi 830099, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1017\/aer.2018.105","article-title":"On-demand assessment of air traffic impact of blocking airspace","volume":"122","author":"Srivastava","year":"2018","journal-title":"Aeronaut. J."},{"key":"ref_2","first-page":"127","article-title":"The concept of airspace","volume":"34","author":"Zhang","year":"2021","journal-title":"J. Beijing Univ. Aeronaut. Astronaut. Soc. Sci. Ed."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"100726","DOI":"10.1016\/j.paerosci.2021.100726","article-title":"Designing airspace for urban air mobility: A review of concepts and approaches","volume":"125","author":"Bauranov","year":"2021","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rosenow, J., Chen, G., Fricke, H., Sun, X., and Wang, Y. (2021). Impact of Chinese and European Airspace Constraints on Trajectory Optimization. Aerospace, 8.","DOI":"10.3390\/aerospace8110338"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"012032","DOI":"10.1088\/1742-6596\/1786\/1\/012032","article-title":"Design of general aviation airspace planning and management system based on Google Earth","volume":"1786","author":"Jing","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1017\/S0373463319000833","article-title":"A Mathematical Programming Approach to Optimum Airspace Sectorisation Problem","volume":"73","author":"Oktal","year":"2020","journal-title":"J. Navig."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhang, K., Liu, Y., Wang, J., Song, H., and Liu, D. (2020, January 8\u201310). Tree-Based Airspace Capacity Estimation. Proceedings of the Integrated Communications Navigation and Surveillance Conference (ICNS), Herndon, VA, USA.","DOI":"10.1109\/ICNS50378.2020.9222986"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"309","DOI":"10.7307\/ptt.v33i2.3645","article-title":"European Airspace (DE)Fragmentation Assessment Model","volume":"33","author":"Rezo","year":"2021","journal-title":"Promet-Traffic Transp."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4814","DOI":"10.1109\/TAES.2020.3003106","article-title":"Optimization-Based Autonomous Air Traffic Control for Airspace Capacity Improvement","volume":"56","author":"Baspnar","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","first-page":"1","article-title":"Network-based airspace model","volume":"20","author":"Zhang","year":"2002","journal-title":"J. China Civ. Aviat. Acad."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gurtner, G., Vitali, S., Cipolla, M., Lillo, F., Mantegna, R.N., Micciche, S., and Pozzi, S. (2014). Multi-scale analysis of the European airspace using network community detection. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0094414"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1049\/iet-ifs.2017.0390","article-title":"Analysis of complex network characteristics and invulnerability of control sectors","volume":"4","author":"Wang","year":"2018","journal-title":"Inf. Secur. Res."},{"key":"ref_13","unstructured":"Gao, J. (2018). Airspace Sector Network Analysis and Survivability Research Based on Complex Network, Civil Aviation University of China."},{"key":"ref_14","first-page":"356","article-title":"Airspace sector network cascade failure resilience and optimization strategy","volume":"39","author":"Qi","year":"2018","journal-title":"J. Aeronaut. Astronaut."},{"key":"ref_15","first-page":"7","article-title":"Modeling and characteristic analysis of complex network of air traffic control sectors","volume":"37","author":"Wang","year":"2019","journal-title":"J. Civ. Aviat. Univ. China"},{"key":"ref_16","first-page":"904","article-title":"Structural characteristic analysis and resilience assessment of airspace sector network","volume":"47","author":"Wang","year":"2021","journal-title":"J. Beijing Univ. Aeronaut. Astronaut."},{"key":"ref_17","first-page":"110","article-title":"Analysis of airspace sector network characteristics and invulnerability based on complex network theory","volume":"2021","author":"Chen","year":"2021","journal-title":"Sci. Technol. Innov."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/0377-2217(90)90056-H","article-title":"An overview of the analytic hierarchy process and its applications","volume":"48","author":"Vargas","year":"1990","journal-title":"Eur. J. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1038\/nbt0308-303","article-title":"What is principal component analysis?","volume":"26","year":"2008","journal-title":"Nat. Biotechnol."},{"key":"ref_20","first-page":"329","article-title":"The use and interpretation of principal component analysis in applied research","volume":"26","author":"Rao","year":"1964","journal-title":"Sankhy\u0101 Indian J. Stat. Ser. A"},{"key":"ref_21","first-page":"3564835","article-title":"Effectiveness of entropy weight method in decision-making","volume":"2020","author":"Zhu","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_22","first-page":"80","article-title":"A review for topology identification of complex networks","volume":"33","author":"Zhou","year":"2017","journal-title":"J. Xi\u2019an Univ. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.3233\/JIFS-17109","article-title":"Concept design and construction algorithm of rough complex networks","volume":"33","author":"Cao","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Pluhacek, M., Senkerik, R., Viktorin, A., and Zelinka, I. (2016, January 7\u20139). Creating Complex Networks Using Multi-Swarm PSO. Proceedings of the 8th International Conference on Intelligent Networking and Collaborative Systems (INCoS), Ostrava, Czech Republic.","DOI":"10.1109\/INCoS.2016.86"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1080\/09720529.2018.1511087","article-title":"Research on target node analysis technology in complex network","volume":"21","author":"Tian","year":"2018","journal-title":"J. Discret. Math. Sci. Cryptogr."},{"key":"ref_26","first-page":"1950067","article-title":"On the Correlation between Fractal Dimension and Robustness of Complex Networks","volume":"27","author":"Wu","year":"2019","journal-title":"Fractals-Complex Geom. Patterns Scaling Nat. Soc."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.physa.2018.02.067","article-title":"An information dimension of weighted complex networks","volume":"501","author":"Wen","year":"2018","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/s12204-017-1798-4","article-title":"Brittleness analysis and important nodes discovery in large time-evolving complex networks","volume":"22","author":"Zhang","year":"2017","journal-title":"J. Shanghai Jiaotong Univ. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"032076","DOI":"10.1088\/1742-6596\/1533\/3\/032076","article-title":"A Community Discovery Algorithm for Complex Networks","volume":"1533","author":"Lv","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1109\/JSYST.2020.2997713","article-title":"Global Reconstruction of Complex Network Topology via Structured Compressive Sensing","volume":"15","author":"Dai","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Yang, X., Wen, S., Liu, Z., Li, C., and Huang, C. (2019). Dynamic Properties of Foreign Exchange Complex Network. Mathematics, 7.","DOI":"10.3390\/math7090832"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1145\/316194.316229","article-title":"On power-law relationships of the internet topology","volume":"29","author":"Faloutsos","year":"1999","journal-title":"ACM SIGCOMM Comput. Commun. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Dudziak-Gajowiak, D., and Juszczyszyn, K. (2019, January 13\u201318). Complex Networks Modelling of Supply Chains in Construction and Logistics. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Rhodes, Greece.","DOI":"10.1063\/1.5114164"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Xu, Y., and Cheng, L. (2017, January 26\u201328). Review of Logistics Networks Structure Based on Complex Networks. Proceedings of the 36th Chinese Control Conference (CCC), Dalian, China.","DOI":"10.23919\/ChiCC.2017.8028546"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Li, M., and Han, J. (2017, January 13\u201314). Complex Network Theory in Urban Traffic Network. Proceedings of the 2nd International Conference on Materials Science, Machinery and Energy Engineering (MSMEE), Dalian, China.","DOI":"10.2991\/msmee-17.2017.175"},{"key":"ref_37","first-page":"701","article-title":"Analysis of characteristics of complex network and robustness in Shanghai metro network","volume":"49","author":"Du","year":"2016","journal-title":"Eng. J. Wuhan Univ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/phys-2017-0001","article-title":"Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory","volume":"15","author":"Zhang","year":"2017","journal-title":"Open Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"100","DOI":"10.3991\/ijoe.v13i03.6863","article-title":"Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure","volume":"13","author":"Zhigang","year":"2017","journal-title":"Int. J. Online Eng."},{"key":"ref_40","first-page":"4346580","article-title":"Research on Evolutionary Mechanism of Agile Supply Chain Network via Complex Network Theory","volume":"2016","author":"Xu","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"ref_41","unstructured":"Yali, Z., Lifu, W., Zhi, K., and Liqian, W. (2018, January 9\u201311). Quantitatively computational controllability of complex networks. Proceedings of the 2018 Chinese Control and Decision Conference, Shenyang, China."},{"key":"ref_42","unstructured":"Li, K., and Sun, Q. (2020, January 11\u201313). Research progress of complex network synchronization control. Proceedings of the International Conference on Intelligent Design (ICID), Xian, China."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Chakraborty, A., Vineeth, B.S., and Manoj, B.S. (2018, January 16\u201319). On the Evolution of Finite-Sized Complex Networks with Constrained Link Addition. Proceedings of the 2018 IEEE International Conference on Advanced Networks and Telecommunications Systems, Indore, India.","DOI":"10.1109\/ANTS.2018.8710101"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.3390\/sym2031683","article-title":"Complex Networks and Symmetry I: A Review","volume":"2","author":"Garlaschelli","year":"2010","journal-title":"Symmetry"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Chen, Y., Zhao, Y., and Han, X. (2019). Characterization of Symmetry of Complex Networks. Symmetry, 11.","DOI":"10.3390\/sym11050692"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"185","DOI":"10.21136\/AM.1978.103744","article-title":"A parallel projection method for linear algebraic systems","volume":"23","author":"Sloboda","year":"1978","journal-title":"Apl. Mat."},{"key":"ref_47","first-page":"99","article-title":"Solving the Parallel Projection Graph of Space Plane Figures","volume":"72","author":"Hu","year":"2001","journal-title":"Comput. Mod."},{"key":"ref_48","first-page":"556","article-title":"Three-dimensional flow field reconstruction based on parallel projection method","volume":"22","author":"Wang","year":"2002","journal-title":"Acta Opt. Sin."},{"key":"ref_49","first-page":"510","article-title":"Algorithm Research and Implementation of Parallel Projection of 3D Graphics","volume":"23","author":"Zhang","year":"1994","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_50","unstructured":"(2006). Procedures for Air Navigation Services: Aircraft Operations (Standard No. ICAO DOC 8168)."},{"key":"ref_51","first-page":"311","article-title":"A Geospatial Data Storage Architecture Design Method Based on GeoSOT Grid","volume":"35","author":"Shan","year":"2018","journal-title":"J. Surv. Mapp. Sci. Technol."},{"key":"ref_52","first-page":"15","article-title":"Airspace rasterization representation method based on GeoSOT grid","volume":"22","author":"Xu","year":"2021","journal-title":"J. Air Force Eng. Univ. Nat. Sci. Ed."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Lu, N., Cheng, C., Jin, A., and Ma, H. (2013, January 21\u201326). An index and retrieval method of spatial data based on GeoSOT global discrete grid system. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium-IGARSS, Melbourne, Australia.","DOI":"10.1109\/IGARSS.2013.6723840"},{"key":"ref_54","first-page":"869","article-title":"GeoSOT grid application for global remote sensing data subdivision and organization","volume":"43","author":"Song","year":"2014","journal-title":"Chin. J. Surv. Mapp."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0270-0255(87)90473-8","article-title":"The analytic hierarchy process\u2014What it is and how it is used","volume":"9","author":"Saaty","year":"1987","journal-title":"Math. Model."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Kuo, T. (2021). An Ordinal Consistency Indicator for Pairwise Comparison Matrix. Symmetry, 13.","DOI":"10.3390\/sym13112183"},{"key":"ref_57","first-page":"125","article-title":"A Review of Research on Flight Conflict Detection and Relief Methods","volume":"5","author":"Sun","year":"2019","journal-title":"Aeronaut. Comput. Technol."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Saaty, T.L. (1980). The Analytic Hierarchy Process, McGraw Hill.","DOI":"10.21236\/ADA214804"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/790\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:52:00Z","timestamp":1760136720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/790"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,11]]},"references-count":58,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["sym14040790"],"URL":"https:\/\/doi.org\/10.3390\/sym14040790","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,4,11]]}}}