BORSA AĞLARININ TOPLULUKLARI İÇİN YENİ BİR TOPOLOJİK ÖLÇÜM

Abstract

Gıda ağları, bilimsel alıntılar, sosyal ağlar, haberleşme ağları, Internet ve borsa ağları gibi interaktif aktörleri içeren sistemler, karmaşık sistemlerin içeriği kapsamı altında pek çok araştırmacı tarafından incelenmiştir. Bu tür sistemler ağırlıklı ağlar tarafından temsil edilir. Aktörler arasındaki yoğun bağlantılar ve ilişkiler, tahmin veya risk analizinde önemli bir rol oynamaktadır. Bu çalışmada, aktif küresel borsa ağının hiyerarşik yapısını ölçmek için yeni bir yaklaşım önerilmiştir. Önerdiğimiz bu yaklaşımda, 21 farklı dünya borsa piyasalarının birbirleriyle ilişkisi Pearson ilişkileri tarafından belirlenmektedir. İlgili hisse senedi ağı belli bir eşik değerine dayanmaktadır. Aynı zamanda, borsa graf topluluklarının tepelerinin etkileşimini karakterize etmek için yeni bir topolojik ölçüm kullanılmaktadır ve bu ölçü 2008 yılı küresel ekonomik krizin zaman dilimleri için incelenmektedir.

Keywords

• Korelasyon Ağları,Ağ Yapılandırması,Minimum Geren Ağaç,Topolojik Ölçüm

A NEW TOPOLOGICAL MEASURE FOR THE COMMUNITIES OF STOCK MARKET NETWORKS

Abstract

Systems involving interactive actors such as food networks, scientific quotations, social networks, communications networks, the Internet and stock exchange networks have long been studied by many researchers under the concept of complex systems. Such systems are represented by weighted networks. The intensive connections and relationships between actors play a crucial role in forecasting or risk analysis. In this study; we propose a new approach to measure the hierarchical structure of the globally active stock market network. In this approach we propose, the relationship of 21 different world stock exchange markets to each other is determined by Pearson's correlations. Relevant stock network is based on a certain threshold value. At the same time, a new topological measure is used to characterize the interaction of the nodes of the graphical communities of the stock market, and this measure is examined for the time periods of 2008 global economic crisis.

Keywords

• Correlation Networks,Network Construction,Minimum Spanning Tree,Topological Measure

References

1. Agarwal, G. and Kempe, D., “Modularity-maximizing graph communities via mathematical programming”. The European Physical Journal B, 66, 3, 409-418, 2008.
2. Balci, M. A. “Fractional virus epidemic model on financial networks”, Open Mathematics, 14, 1, 1074-1086 2016.
3. Balci, M. A. “Hierarchies in Communities of Borsa Istanbul Stock Exchange”, Hacettepe Journal of Mathematics and Statistics, In Press, DOI:10.15672/hjms.201614520777.
4. Bankevich, A. V. “Bounds of the number of leaves of spanning trees in graphs without triangles”. Journal of Mathematical Sciences, 184, 5, 557-563, 2012.
5. Bollobas, B. Graph theory: an introductory course. Vol. 63. Springer Science & Business Media, 2012.
6. Centola, D. and van de Rijt, A. “Choosing your network: Social preferences in an online health community”. Social science & medicine, 125, 19-31, 2015.
7. Chan, T. F., S. Osher, and Shen,J. "The Digital TV Filter and Nonlinear Denoising." IEEE Transactions on Image Processing, 10, 2, 231-241, 2001.
8. Chug, F. R. K. Spectral Graph Theory, American Mathematical Society (1997).

9. Evans, T.S., “Clique graphs and overlapping communities”, Journal of Statistical Mechanics: Theory and Experiment, 12, P12037, 2009.
10. Everett, M.G. and Borgatti, S.P., “Analyzing clique overlap”, Connections, 21, 1, 49-61., 1998.
11. Gross, J. L., and Yellen J., eds. Handbook of graph theory. CRC press, 2004.
12. Guler, H., Dundar, P., and Balci, M. A.“Solitude Number at Graphs”, IJ Pure and Applied Mathematics, 66, 3, 355-364, 2011.
13. Hur, S-W. and Lillis, J., "Relaxation and Clustering in a Local Search Framework: Application to Linear Placement.", Proceedings - Design Automation Conference, 1999, 360-366.
14. Jang, W., Lee, J., and Chang, W. “Currency crises and the evolution of foreign exchange market: evidence from minimum spanning tree”, Physica A, 390, 707–718, 2011.
15. Lancichinetti, A., Santo F., and Kertész, J. "Detecting the overlapping and hierarchical community structure in complex networks." New Journal of Physics 11, no. 3, 033015, 2009.
16. Morel, B. and Ramanujam, R., "Through the Looking Glass of Complexity: The Dynamicsof Organizations as Adaptive and Evolving Systems." Organization Science, 10 , 3, 278-293, 1999.
17. Newman, M.E.,”Detecting community structure in networks.” The European PhysicalJournal B-Condensed Matter and Complex Systems, 38,2, 321-330, 2004.
18. Newman, M.E.,”Fast algorithm for detecting community structure in networks.” Physicalreview E, 69, 6 066133, 2004.
19. Newman, M.E. and Girvan, M., “Finding and evaluating community structure in networks”. Physical review E, 69, 2, p.026113, 2004.
20. Newman, M. E. “The structure and function of complex networks”, SIAM review, 45, 2, 167-256, 2003.
21. Onnela, J.-P., Chakraborti, A., and Kaski, K. “Dynamic asset trees and portfolio analysis”, The European Physical Journal B, 30, 285–288, 2002.
22. Onnela, J.-P., Chakraborti, A. and Kaski, K. “Dynamics of market correlations: taxonomy and portfolio analysis”, Physical Review E, 68, 056110, 2003.
23. Ozkanlar, A. and Clark, A. E., "ChemNetworks: A Complex Network Analysis Tool for Chemical Systems." Journal of Computational Chemistry 35, 6, 495-505, 2014.
24. West, D. B.,Introduction to graph theory. Vol. 2. Upper Saddle River: Prentice hall, 2001.