**5. Conclusions**

The presented study investigates the cross-correlations among currency exchange rates on Forex market by the PLCS algorithm, followed by network analysis. The PLCS method is focused on the trend correlations and unlike other methods, allows to observe crosscorrelation of trends. The results of this paper show that crises influence trend correlations. The convergen<sup>t</sup> and divergent networks are not simple mirrors of each other. Because the network is constructed with the cross-correlation matrix, the introduced constraint may reveal a different feature, e.g., the community number observed in the converging network presents a two-state evolution that is rarely observed in a diverging network. Particularly interesting is the biggest cluster size analysis, which is sensitive to crisis occurrence. Particularly, the change of the cluster size can expose the severity crisis. The third feature investigated here is the frequency of the connection, which verifies the stability of the connection. Currencies are forming groups concerning the frequency of connections to the network. It might give an opportunity to develop a new classification of currencies with respect to their relationship to the group. The last performed analysis—the rank node histogram evolution—provides the most detailed information about the structure and evolution of the cross-correlation among currencies. The analysis of the rank node entropy is particularly interesting. The obtained results sugges<sup>t</sup> that entropy might be a synthetic measure of crisis. Of course, this conclusion needs further analysis, but the presented results are very promising.

A very special outcome of this analysis is that, in recent times, e.g., 2017, the structure of the observed networks has changed and depending on the type of the network (converging or diverging) the high or low-rank nodes are prevailing. It means that the cross-correlation in the Forex market has changed significantly. The observed changes in the biggest clique size and the number of communities are the results of globalisation, which are more transparent during crises. In this special condition, correlations and mutual dependence are exposed. Of course, the results depend on the choice of central currency and the analysis can be repeated for other central currencies. However, the main aim of this paper was establishing new analysis methods, so the detailed analysis of the role of the central currency choice is left for other studies. The additional results are the analysis of the role of the time window length. The presented results allow for estimating the window size with the requested quality of research. It is not recommended to use time windows shorter than 20 days. Of course, extending the size of the time window improves the quality of the results from the statistical point of view, and it filters the high frequency changes exposing the long-term proprieties. Although this aspect was not discussed here, longer time windows might be more appropriate for forecasting.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.
