The Structure of the Local Supercluster of Galaxies Revealed by the Three-Dimensional Voronoi's Tessellation Method

3D Voronoi's tessellation method was first applied to identify groups of galaxies in the structure of a supercluster. The sample under consideration consists of more than 7000 galaxies of the Local Supercluster (LS) with radial velocities up to 3100 km/s. Because of an essential non-homogeneity of the LS catalogue, it was proposed to overscale distances in such an ''artificial'' way that the concentration of galaxies was varying as with increase of the distance a power-behaved function with the same exponent beta as for the full homogeneous catalogue. Various parameters of clustering were taking into account: alpha (0.01, 0.1, 1%) as the part of galaxies, which have the relative volume of a Voronoi's cell smaller than the critical one for the random distribution; beta = 0, which fits to the random galaxy distribution; beta = 0.7, which is close to the pancake galaxy distribution. It is revealed that Voronoi's tessellation method depends weakly on beta-parameter, and the number of galaxies in rich structures is growing rather than in poor ones with increase of alpha-parameter. The comparison of the groups derived with the groups obtained by Karachentsev's dynamical method shows that the number of groups, which coincides by all the components, is 22%. As a whole, the dynamical method is more preferred for identifying sparsely populated galaxy groups, whereas 3D Voronoi's tessellation method is preferred for more populated ones.