## 3 Results
The median errors of common points in the isometric and conformal transformations were 0.13 mm/y, and for the affine transformation, they were 0.12 mm/yr. From the point of view of vertical movements of the Earth's crust, all transformation methods can be considered suitable. However, the differences (Table 6) are smallest when using a 12-parameter affine transformation. At 50 adjustment points, the differences in vertical movements did not exceed 0.2 mm/yr compared to the equalized values. Figure 12: Spatial distribution of differences between vertical movements in the hybrid network versions 1 and 2) (source: own study). Version 2 of the hybrid network equalization showed that the average errors after equalization do not differ significantly from those from the adjustment in version 1, but their distribution is more similar to the normal distribution. In version 2 of the transformation, the average unit error m\({}_{0}\) is the smallest for the affine transformation. The isometric and conformal transformations are characterized by the same error 3x greater than the m\({}_{0}\) of the affine transformation. Similarly, the affine transformation error is 3x smaller than in the other cases. For the isometric and conformal transformations, the median is the same regardless of the application of the Hausbrandt correction, similarly to version 1. For the affine transformation, the median was 0.27 mm/yr. The median errors of common points in the isometric and conformal transformations were 0.25 mm/yr (worse compared to version 1), and 0.12 mm/yr for the affine transformation (they did not change compared to version 1). Regardless of the use of the Hausbrandt correction, statistically, the results are the same for both conformal and affine transformations. The smallest differences between the DLN network and the hybrid network were obtained in version 2 (11 common points), from 0.1 mm/yr to \(-\)0.8 mm/yr. The differences (Figure 11) between the GTN network and the hybrid network version 1 do not exceed 1 mm/yr, while between the hybrid network version 2, they do not exceed 0.5 mm/yr. The smallest differences between the GTN network and the hybrid network were obtained in version 2. Between the two versions of the hybrid network, the maximum vertical movements differences range from 2.6 mm/yr to 1.5 mm/yr. Tables 5-7 show that the smallest transformation errors and consistency with the hybrid network (versions 1 and 2) are obtained using the 12-parameter affine transformation method with Hausbrandt correction. The comparison of vertical movements from the affine transformation and hybrid network adjustment (Figure 13) shows that the biggest differences are in vertical movements for version 1; in version 2, there is much better  
Figure 13: Spatial distribution of vertical movements difference between affine transformation and hybrid network adjustment (version 1—(**a**); version 2—(**b**)) (source: own study). consistency in the results. The largest vertical movements differences for version 1 of the affine transformation and the hybrid network are at stations identified as outliers. An analysis of the impact of the distribution of adjustment points on the example of affine transformation showed that reducing the number of adjustment points did not increase the transformation errors, even though the adjustment points were not evenly distributed across the study area. The transformation errors increased most for the ELBL station, SIPC, and WLBR (approximately 0.2 mm/yr), while in the remaining area, they ranged from 0.0 mm/yr to 0.1 mm/yr. The application of the theory of scale-free networks allowed for the selection of points that have the most significant impact on the structure of the network and are not random. Reducing the number of adjustment points did not affect the quality of the transformation or cause a local adjustment effect. The hybrid network adjustment of version 2 with 11 connection points had smaller errors than version 1 with 50 points.