{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T21:17:33Z","timestamp":1772054253278,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T00:00:00Z","timestamp":1711324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Structural properties of the currency market were examined with the use of topological networks. Relationships between currencies were analyzed by constructing minimal spanning trees (MSTs). The dissimilarities between time series of currency returns were measured in various ways: by applying Euclidean distance, Pearson\u2019s linear correlation coefficient, Spearman\u2019s rank correlation coefficient, Kendall\u2019s coefficient, partial correlation, dynamic time warping measure, and Kullback\u2013Leibler relative entropy. For the constructed MSTs, their topological characteristics were analyzed and conclusions were drawn regarding the influence of the dissimilarity measure used. It turned out that the strength of most types of correlations was highly dependent on the choice of the numeraire currency, while partial correlations were invariant in this respect. It can be stated that a network built on the basis of partial correlations provides a more adequate illustration of pairwise relationships in the foreign exchange market. The data for quotations of 37 of the most important world currencies and four precious metals in the period from 1 January 2019 to 31 December 2022 were used. The outbreak of the COVID-19 pandemic in 2020 and Russia\u2019s invasion of Ukraine in 2022 triggered changes in the topology of the currency network. As a result of these crises, the average distances between tree nodes decreased and the centralization of graphs increased. Our results confirm that currencies are often pegged to other currencies due to countries\u2019 geographic locations and economic ties. The detected structures can be useful in descriptions of the currency market, can help in constructing a stable portfolio of the foreign exchange rates, and can be a valuable tool in searching for economic factors influencing specific groups of countries.<\/jats:p>","DOI":"10.3390\/e26040279","type":"journal-article","created":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T12:40:11Z","timestamp":1711370411000},"page":"279","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Impact of the Measure Used to Calculate the Distance between Exchange Rate Time Series on the Topological Structure of the Currency Network"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9598-844X","authenticated-orcid":false,"given":"Joanna","family":"Andrzejak","sequence":"first","affiliation":[{"name":"Institute of Civil Engineering, Warsaw University of Life Sciences\u2014SGGW, 02-787 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9725-2479","authenticated-orcid":false,"given":"Leszek J.","family":"Chmielewski","sequence":"additional","affiliation":[{"name":"Institute of Information Technology, Warsaw University of Life Sciences\u2014SGGW, 02-776 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7286-8536","authenticated-orcid":false,"given":"Joanna","family":"Landmesser-Rusek","sequence":"additional","affiliation":[{"name":"Institute of Economics and Finance, Warsaw University of Life Sciences\u2014SGGW, 02-787 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6755-1830","authenticated-orcid":false,"given":"Arkadiusz","family":"Or\u0142owski","sequence":"additional","affiliation":[{"name":"Institute of Information Technology, Warsaw University of Life Sciences\u2014SGGW, 02-776 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"531","DOI":"10.12693\/APhysPolA.114.531","article-title":"Minimal Spanning Tree graphs and power like scaling in FOREX networks","volume":"114","year":"2008","journal-title":"Acta Phys. 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