AIR TRAFFIC ANALYSIS OF COUNTRIES WITH RENYI ENTROPY

Yıl 2019, Cilt: 7 Sayı: 4, 843 - 853, 19.12.2019

İhsan Tuğal , Ali Karcı

https://doi.org/10.21923/jesd.497454

Öz

Centrality is one of the most frequently
studied subjects of social network analysis. The identification of the most
effective entities in a network or system can be found by measures of
centrality. In this study, using the data of air traffic with Renyi entropy,
the most influential countries in this field were analyzed in the graph
structure. The most effective countries in air traffic were identified. It has
been shown that centrality measurements can be made with Renyi entropy in a
weighted and directional network. A method for the detection of vital nodes in
a network was proposed. Difference from Shannon, it was observed that results
could be obtained for different situations by using the α coefficient in Renyi.
Sometimes measuring only the effect of edge weight or node degree does not
yield accurate results. Using α to adjust this effect has enabled us to get
more accurate results.

Anahtar Kelimeler

Air Traffic, Complex Networks, Graphs, Renyi Entropy, Node Centrality

RENYI ENTROPI ILE ÜLKELERİN HAVA TRAFİĞİNİN ANALİZİ

Öz

Merkezilik sosyal ağ analizi yapan
kişilerin en çok çalıştığı konulardan biridir. Bir ağdaki en etkili ve sisteme
etkisi olan varlıkların tespiti merkezilik ölçüleri ile bulunabilir. Bu
çalışmada Renyi entropi ile havayolu trafiği verileri kullanılarak bu alandaki
en etkili ülkeler çizge yapısında analiz edildi. Hava trafiğinde en merkezi
ülkeler tespit edildi. Ağırlıklı ve yönlü bir ağda Renyi entropi ile merkezilik
ölçümlerinin yapılabileceği gösterildi. Bir ağdaki hayati öneme sahip
düğümlerin tespiti için bir yöntem önerildi. Shannon’dan farklı olarak Renyi’de
α katsayısı kullanılarak farklı durumlar için sonuç elde edilebileceği görüldü.
Sadece kenar ağırlıklarının veya düğüm derecelerinin etkisinin ölçülmesi bazen
doğru sonuçlar vermediği için α’nın bu etkiyi ayarlamak için kullanılması daha
doğru sonuçlar almamızı sağladı.

Anahtar Kelimeler

Havayolu, Kompleks Ağlar, Çizgeler, Renyi Entropi, Düğüm Merkeziliği

Kaynakça

• Alexanderson, G. L. (2006). About the cover: Euler and Königsberg’s bridges: A historical view. Bulletin of the American Mathematical Society. https://doi.org/10.1090/S0273-0979-06-01130-X
• Bromiley, P. A., Thacker, N. A., & Bouhova-Thacker, E. (2004). Shannon entropy, Renyi entropy, and information. Erişim Tarihi: 14 Aralık 2018, website: http://www.tina-vision.net/docs/memos/2004-004.pdf
• Cong, W., Hu, M., Dong, B., Wang, Y., & Feng, C. (2016). Empirical analysis of airport network and critical airports. Chinese Journal of Aeronautics, 29(2), 512–519. https://doi.org/10.1016/j.cja.2016.01.010
• Dehmer, M., & Mowshowitz, A. (2011). A history of graph entropy measures. Information Sciences, 181(1), 57–78. https://doi.org/10.1016/j.ins.2010.08.041
• Du, Y., Gao, C., Hu, Y., Mahadevan, S., & Deng, Y. (2014). A new method of identifying influential nodes in complex networks based on TOPSIS. Physica A: Statistical Mechanics and Its Applications, 399, 57–69. https://doi.org/10.1016/j.physa.2013.12.031
• Ernesto, T. (1956). A note on the information content of graphs. The Bulletin of Mathematical Biophysics, 18(2), 129–135.
• Everett, M. G., & Borgatti, S. P. (2005). Extending Centrality. In P. J. Carrington, J. Scott, & S. Wasserman (Eds.), Models and Methods in Social Network Analysis (pp. 57–76). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511811395.004
• Fei, L., & Deng, Y. (2017). A new method to identify influential nodes based on relative entropy. Chaos, Solitons and Fractals, 104, 257–267. https://doi.org/10.1016/j.chaos.2017.08.010
• Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239. https://doi.org/10.1016/0378-8733(78)90021-7
• Hartley, R. V. L. (1928). Transmission of Information. Bell System Technical Journal, 535. https://doi.org/10.1109/83.748891
• http://www.visualizing.org/datasets/global-flights-network. (n.d.). Global Flight Network Data. Erişim Tarihi: 11 Ekim 2018, from https://github.com/gsmanu007/Complex-network-analysis-of-Airport-network-data
• Leskovec, J., Rajaraman, A., & Ullman, J. D. (2014). Mining of massive datasets: Second edition. Mining of Massive Datasets: Second Edition. https://doi.org/10.1017/CBO9781139924801
• Moreno, J. L. (1934). Who Shall Survive? A New Approach to the Problem of Human Interrelations. Nervous and Mental Disease Publishing (Vol. 58). https://doi.org/10.2307/2084777
• Mowshowitz, A. (1968). Entropy and the complexity of graphs: I. An index of the relative complexity of a graph. The Bulletin of Mathematical Biophysics, 30(1), 175–204. https://doi.org/10.1007/BF02476948
• Nie, T., Guo, Z., Zhao, K., & Lu, Z. M. (2016). Using mapping entropy to identify node centrality in complex networks. Physica A: Statistical Mechanics and Its Applications, 453, 290–297. https://doi.org/10.1016/j.physa.2016.02.009
• Rashevsky, N. (1955). Life, information theory, and topology. The Bulletin of Mathematical Biophysics, 17(3), 229–235. https://doi.org/10.1007/BF02477860
• Rényi, A. (1961). On measures of entropy and information. In Fourth Berkeley Symposium on Mathematical Statistics and Probability (p. 547). https://doi.org/10.1021/jp106846b
• Shannon, C. E. (1951). Prediction and Entropy of Printed English. Bell System Technical Journal, 30(1), 50–64. https://doi.org/10.1002/j.1538-7305.1951.tb01366.x
• Tutzauer, F. (2007). Entropy as a measure of centrality in networks characterized by path-transfer flow. Social Networks, 29(2), 249–265. https://doi.org/10.1016/j.socnet.2006.10.001
• Wang, S., Du, Y., & Deng, Y. (2017). A new measure of identifying influential nodes: Efficiency centrality. Communications in Nonlinear Science and Numerical Simulation, 47, 151–163. https://doi.org/10.1016/j.cnsns.2016.11.008
• Wikipedia.org. (n.d.). https://tr.wikipedia.org/wiki/Termodinamik Erişim Tarihi 19 Temmuz 2018.