## 2 Observational Data  
Because our method is new, we decided to test it on a well-known and tested sample of galaxies and their structures, in order to free ourselves from not fully controlled observational and systematic effects. As part of the implementation of the method, the Tully Nearby Galaxies (NBG) Catalog [36] was used. This catalog was chosen because it contains all the necessary information about both individual galaxies and their structures. In particular, it has been carefully screened for the completeness of the sample and the removal of non-galactic objects from it. One should note that the NBG Catalog is complete up to the magnitude limit \(B_{T}^{b,i}=12.0\)[41]. Additionally, it includes dimmer, low-surface brightness gas-rich galaxies (late-type spirals), ensuring that all more massive galaxies are taken into account. Due to the position of the Galaxy with respect to the center of the Local Supercluster (LSC), which is the Virgo Cluster, it is complete for such objects only up to the Virgo Cluster center. The Catalog contains 2367 galaxies with radial velocities (corrected to the motion of the Sun) lower than 3000 \(\frac{\rm km}{\rm s}\) and devoid of background objects. The Tully Catalog provides relatively even coverage of the entire unobstructed sky [41]. Position angles not included in the catalog were taken from [42; 43; 44; 45], and missing measurements were made on Palomar Sky Survey prints by Flin [8]. For face-on galaxies, for which it was impossible to determine the position angles, their random distribution was assumed (for face-on galaxies, the value of the position angles has a minimal effect on the orientation of the galaxy space--see the next chapter). The catalog contains information on the morphological types of galaxies, therefore, it enables qualitative verification of the effectiveness of the proposed method. The NBG catalog also lists galaxy group and subgroup affiliations for all galaxies in the catalog. Groups were selected in a uniform way based on angular and distance separation. [PERSON] selected 366 groups of two or more members involving 1525 galaxies (64% of all NBG galaxies) [41]. The distances of galaxies are determined by velocity, assuming the Einstein de Sitter model or the flat dust model with the deceleration parameters \(q_{0}=1/2\) (for historical reasons, \(q_{0}\) denotes the deceleration parameter in this case) and \(H_{0}=75{\rm km\ s}^{-1}{\rm Mpc}^{-1}\), as well as the velocity perturbation model near the Virgo Cluster [46]. The use of the simpler Einstein de Sitter model instead of \(\Lambda\)CDM is justified, because the range of the NBG catalog [36] is \(z=0.01\), and up to distances corresponding to \(z=0.2\), the differences between the distances calculated in different cosmological models are minimal. This means that the distances of the galaxies are determined in a very good and homogeneous way. As a result, lists of galaxies included in particular galaxy groups are free from foreground and background objects, which is essential when analyzing small numbers of galaxy structures. In our opinion, the groups selected according to the precise criteria in the Tully catalog are an example of one of the best group selections. The use of the catalog in other research works [8; 47; 48; 49] also makes it possible to indicate the correlation of the obtained results. In the present work, during the implementation of the method, only those groups from the NBG Catalog that have at least 40 members are used. There are 18 such groups.