Comparison of two types of topological networks for the foreign exchange market: one based on correlation coefficients and the other on the concept of causality

Joanna  Landmesser-Rusek

doi:https://doi.org/10.59139/stattrans-2026-023

Comparison of two types of topological networks for the foreign exchange market: one based on correlation coefficients and the other on the concept of causality

Joanna Landmesser-Rusek Institute of Economics and Finance, Warsaw University of Life Sciences—SGGW, Warsaw, Poland ORCID:https://orcid.org/0000-0001-7286-8536 Statistics in Transition new series, vol. 27, 2026, 2, pages: 185-204 Published online: 9 June 2026 https://doi.org/10.59139/stattrans-2026-023 Citation: Landmesser-Rusek J., 2026. Comparison of two types of topological networks for the foreign exchange market: one based on correlation coefficients and the other on the concept of causality. Statistics in Transition new series, 27(2), pp. 185-204. https://doi.org/10.59139/stattrans-2026-023

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ABSTRACT

Topological networks make it possible to recognize structural properties of the currency market. Such networks can be constructed on the basis of the values of correlation coefficients between currency pairs, and the popular minimum spanning tree (MST) algorithm allows an understanding of significant relationships on the market. An alternative measure of distance, based on the concept of causality for time series, makes it possible to measure not only the strength of relationships between currency pairs but also the directionality of these relationships. There is even an equivalent of MST on a directed graph ? minimum-cost arborescence (MCA). The purpose of this study is to compare correlation and causality networks built for the foreign exchange market. The networks were constructed in a stepwise manner for the most important world currencies in the period from 3rd Jan. 2020 to 18th Oct. 2024. The comparison was carried out using certain topological characteristics of the networks, such as density, average distance, diameter, centralization index and degrees of vertices. The study details the properties of both approaches.

KEYWORDS

topological networks, foreign exchange market, correlation, causality.

REFERENCES

Albert, R., Jeong, H., Barabási, A.-L., (2000). Error and attack tolerance of complex networks. Nature, Vol. 406, pp. 378–382.

Andrzejak, J., Chmielewski, L. J., Landmesser-Rusek, J. and Orłowski, A., (2024). The impact of the measure used to calculate the distance between exchange rate time series on the topological structure of the currency network. Entropy, Vol. 26, pp.1–17.

Barabási, A.-L., Bonabeau, E., (2003). Scale-free networks. Scientific American, Vol. 288, pp. 60–69.

Basnarkov, L., Stojkoski, V., Utkovski, Z. and Kocarev, L., (2019). Correlation Patterns in Foreign Exchange Markets. Physica A: Statistical Mechanics and its Applications, Vol. 525, pp. 1026–1037.

Billio, M., Getmansky, M., Lo, A. W. and Pelizzon, L., (2012). Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, Vol. 104, pp. 535–559.

Bullmore, E., Sporns, O., (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience, Vol. 10, pp. 186–198.

Cao, H., Guo, Z., Li, Y. and Ran, Z., (2020). The Relationship Structure of Global Exchange Rate Based on Network Analysis. Journal of Mathematical Finance, Vol. 10, pp. 58–76.

Cohen, R., Erez, K., ben-Avraham and D., Havlin, S., (2000). Resilience of the Internet to Random Breakdowns. Physical Review Letters, Vol. 85, pp. 4626–4628.

Feng, X., Wang, X., (2010). Evolutionary topology of a currency network in Asia. International Journal of Modern Physics C, Vol. 21, pp. 471–480.

Fortunato, S., (2010). Community detection in graphs. Physics Reports, Vol. 486, pp. 75–174.

Górski, A. Z., Drożdż, S., Kwapień, J. nad Oświęcimka, P., (2008). Minimal Spanning Tree graphs and power like scaling in FOREX networks. Acta Physica Polonica A, Vol. 114, pp. 531–538.

Granger, C. W. J., (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, Vol. 37, pp. 424–438.

Granger, C. W. J., (1980). Testing for causality: A personal viewpoint. Journal of Economic Dynamics and Control, Vol. 2, pp. 329–352.

Gupta, K., Chatterjee, N., (2020). Examining Lead-Lag Relationships In-Depth, with Focus on FX Market as COVID-19 Crises Unfolds, arXiv, arXiv:2004.10560.

Hidalgo, C. A., Rodriguez-Sickert, C., (2008). The dynamics of a mobile phone network. Physica A: Statistical Mechanics and its Applications, Vol. 387, pp. 3017–3024.

Jang, W., Lee, J. and Chang, W., (2011). Currency crises and the evolution of foreign exchange market: Evidence from minimum spanning tree. Physica A: Statistical Mechanics and its Applications, Vol. 390, pp. 707–718.

Jiang, Z., Arreola Hernandez, J., McIver, R. P. and Yoon, S.-M., (2022). Nonlinear Dependence and Spillovers between Currency Markets and Global Economic Variables. Systems, Vol. 10, 80.

Kazemilari, M., Mohamadi, A., (2018). Topological Network Analysis Based on Dissimilarity Measure of Multivariate Time Series Evolution in the Subprime Crisis, International Journal of Financial Studies, Vol. 6, 47.

Kenett, D. Y., Tumminello, M., Madi, A., Gur-Gershgoren, G., Mantegna, R. N. and Ben-Jacob, E., (2010). Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market. PLoS ONE, Vol. 5, e15032.

Kruskal, J. B., (1956). On the shortest spanning subtree of a graph and the travelling salesman problem. Proceedings of the American Mathematical Society, Vol. 7, pp. 48–50.

Kwapień, J., Gworek, S. and Drożdż, S., (2009). Structure and Evolution of the Foreign Exchange Networks. Acta Physica Polonica B, Vol. 40, pp. 175–194.

Liu, J., Wu, J. and Yang, Z. R., (2004). The spread of infectious disease on complex networks with household-structure. Physica A: Statistical Mechanics and its Applications, Vol. 341, pp. 273–280.

Liu, J., Xiong, Q., Shi, W., Shi, X. and Wang, K., (2016). Evaluating the importance of nodes in complex networks. Physica A: Statistical Mechanics and its Applications, Vol. 452, pp. 209–219.

Mantegna, R. N., (1999). Hierarchical structure in financial markets. The European Physical Journal B: Condensed Matter and Complex Systems, Vol. 11, pp. 193–197.

Mantegna, R. N., Stanley, H. E., (1999). Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge.

Marti, G., Nielsen, F., Bińkowski, M. and Donnat, P., (2021). A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets. In: Progress in Information Geometry. Signals and Communication Technology; Nielsen, F., (Ed); Springer: Cham, Switzerland.

McDonald, M., Suleman, O., Williams, S., Howison, S. and Johnson, N., (2005). Detecting a Currency’s Dominance or Dependence using Foreign Exchange Network Trees. Physical Review E, Vol. 72, 046106.

Miśkiewicz, J., (2021). Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market. Entropy, Vol. 23, pp. 1–19.

Mizuno, T., Takayasu, H. and Takayasu, M., (2006). Correlation networks among currencies. Physica A: Statistical Mechanics and its Applications, Vol. 364, pp. 336–342.

Naylor, M. J., Rose, L. C. and Moyle, B. J., (2007). Topology of foreign exchange markets using hierarchical structure methods. Physica A: Statistical Mechanics and its Applications, Vol. 382, pp. 199–208.

Ortega, G. J., Matesanz, D., (2006). Cross-country hierarchical structure and currency crises. International Journal of Modern Physics C, Vol. 17, pp. 333–341.

Palla, G., Barabási, A. and Vicsek, T., (2007). Quantifying social group evolution, Nature, Vol. 446, pp. 664–667.

Park, J. H., Chang, W. and Song, J. W., (2020). Link prediction in the Granger causality network of the global currency market. Physica A: Statistical Mechanics and its Applications, Vol. 553, 124668.

Porter, M. A.; Onnela, J.-P. and Mucha, P. J., (2009). Communities in Networks. Notices of the American Mathematical Society, Vol. 56, pp. 1082–1097, 1164–1166.

Výrost, T., Lyócsa, Š. and Baumöhl, E., (2015). Granger causality stock market networks: Temporal proximity and preferential attachment. Physica A: Statistical Mechanics and its Applications, Vol. 427, pp. 262–276.

Wang, G. J., Xie, C., Han, F. and Sun, B., (2012). Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree. Physica A: Statistical Mechanics and its Applications, Vol. 391, 4136–4146.

Watts, D., Strogatz, S., (1998). Collective dynamics of ‘small-world’ networks. Nature, Vol. 393, pp. 440–442.

Wu, J.-J., Gao, Z.-Y. and Sun, H.-J., (2008). Optimal traffic networks topology: A complex networks perspective. Physica A: Statistical Mechanics and its Applications, Vol. 387, pp. 1025–1032.