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1. Introduction

Galaxies and systems of galaxies form due to initial density perturbations of different scale. Short perturbations with a wavelength of several Mpc give rise to the formation of individual galaxies and small systems of galaxies, medium scale perturbations lead to the formation of clusters of galaxies, and so on. Perturbations of a characteristic scale of tex2html_wrap_inline1621 htex2html_wrap_inline1623 Mpc can be related to superclusters of galaxies. Still larger perturbations have much lower amplitude and thus they only modulate densities and masses of smaller systems (Frisch et al.  1995). Therefore superclusters of galaxies are the largest relatively isolated density enhancements in the Universe.

The presence of superclusters is known since the pioneering studies of Shapley (1930). The nearest example is the Local Supercluster with the Virgo cluster as the central cluster (de Vaucouleurs 1956). Other nearby examples are the Perseus-Pisces supercluster which consists of the Perseus chain of rich clusters, and the Coma supercluster with the Coma cluster and A1367 forming its double center. The distribution of galaxies in superclusters is filamentary, these filaments can contain as density enhancements groups and clusters galaxies of different richness (Gregory & Thompson 1978; Jõeveer et al.  1978; Einasto et al.  1984).

Superclusters are not completely isolated in space. Galaxy and cluster filaments connect neighbouring superclusters to a single network. Filaments joining the Local and Perseus-Pisces superclusters were noticed by Einasto et al.  1980, and filaments joining the Local and Coma superclusters by Zeldovich et al. (1982) and Tago et al. (1984, 1986). A section of the Great Wall (Geller & Huchra 1989) is a filamentary system which joins the Coma and Hercules superclusters (Lindner et al.  1995).

We shall use the term supercluster-void network for the web of filaments, clusters, and voids which extends over the whole observable part of the Universe. The formation of a filamentary web of galaxies and clusters is predicted in any physically motivated scenario of structure formation (of recent works we mention studies by Bond et al. 1996 and Katz et al.  1996). Properties of this network depend on the density perturbations of medium and large wavelengths. Thus the study of the properties of the supercluster-void network yields information on the shape of the initial power spectrum on these wavelengths. Of particular interest is the region of transition from the Harrison-Zeldovich spectrum with positive power index n=1 on very large scales to galactic scales with negative effective power index tex2html_wrap_inline1627. In this wavelength region differences between various structure formation scenarios are the largest.

Our present series of papers is devoted to the study of the properties of the supercluster-void network. Superclusters can be determined using the appropriately smoothed density field, or using discrete tracers, such as galaxies or clusters of galaxies, and applying the clustering analysis. In both cases superclusters can be defined as the largest non-percolating systems of galaxies or clusters of galaxies. Decreasing the threshold density or increasing the neighbourhood radius we get already a percolating system - the supercluster-void network. Both galaxies and clusters are concentrated to superclusters and trace similar high-density regions of the Universe (Oort 1983; Bahcall 1991). In detail the distributions are different, since clusters of galaxies trace only compact high-density regions - the skeleton of the structure. The use of galaxies as tracers of superclusters is limited to relatively small distances as catalogues of redshifts of galaxies which cover a large fraction of the sky are not deep and complete enough yet. On the contrary, the catalogues of rich clusters of galaxies by Abell (1958) and Abell et al.  (1989, ACO), which cover the whole sky out of the Milky Way zone of avoidance, are thought to be fairly complete up to distances of several hundred megaparsecs. Thus most supercluster studies were based on these catalogues of clusters of galaxies.

Catalogues of superclusters using clusters as structure tracers have been compiled by Bahcall & Soneira (1984); Batuski & Burns (1985); West (1989); Postman et al. (1992). The first whole-sky supercluster catalogues were prepared by Zucca et al.  (1993, hereafter ZZSV); Einasto et al.  (1994, hereafter  EETDA); and Kalinkov & Kuneva (1995), the last one uses mainly clusters with estimated redshifts.

In the study of the distribution of superclusters it is of central importance to know whether it deviates from a random distribution, and if yes, whether the supercluster distribution defines a certain scale in the Universe. These questions were addressed already by Oort (1983). Subsequent studies have shown the presence of some regularities in the distribution of superclusters. Zeldovich et al. (1982) and Tully (1986, 1987) demonstrated that nearby superclusters are concentrated to a plane which almost coincides with the plane of the Local Supercluster. This concentration of superclusters forms a wall dividing two huge voids, the Northern and Southern Local voids (Einasto & Miller 1983; Lindner et al.  1995). Tully et al.  (1992) showed that several superclusters are almost perpendicular to Local Supercluster plane. EETDA suggested that superclusters and voids form a quite regular network with a characteristic distance between superclusters of about 110 - 140 htex2html_wrap_inline1631 Mpc. A similar scale was found by Mo et al.  (1992) in the distribution of clusters of galaxies; the value is also close to that found by Broadhurst et al.  (1990) for the distance between peaks in the redshift distribution of galaxies in a pencil-beam survey of galaxies and. The scale of about 100 htex2html_wrap_inline1633 Mpc  has also been found in the distribution of QSO absorption line systems (Quashnock et al. 1996). These results suggest the presence of a peak in the power spectrum of density fluctuations at the corresponding wavelength (Einasto & Gramann 1993; Frisch et al.  1995). An excess power in the power spectrum of galaxies of the Las Campanas redshift survey has been detected at this scale by Landy et al.  (1996).

In recent years the number of clusters with measured and re-measured redshifts has been increased considerably. Thus a new and more detailed analysis of the distribution of clusters and superclusters is possible. In this series of papers we shall construct a new catalogue of superclusters, study the large-scale distribution of superclusters (the present paper), determine the correlation function and the power spectrum of clusters of galaxies , , (Einasto et al.  1997a-c), investigate the form and orientation of superclusters (Jaaniste et al.  1997), compare the distribution of clusters and superclusters of galaxies with the distribution of similar objects in numerical simulations (Frisch et al.  1997), and investigate consequences of these results to scenarios of structure formation , (Einasto et al.  1997a,b).

The present paper is arranged as follows. Section 2 presents a new catalogue of superclusters up to z = 0.12. Redshift data are available for 2/3 of the clusters within this distance limit. We use this limit in order to include very rich superclusters missed in the earlier version of the catalogue (EETDA). In addition, we apply improved distance estimates for clusters without observed redshifts (Peacock & West 1992). In Sect. 3 we determine the selection function and mean space density of clusters. In Sect. 4 we describe catalogues of randomly located superclusters. In Sect. 5 we use the catalogue of superclusters to describe and analyse the structures delineated by superclusters on large scales, and compare the spatial distribution of rich and poor superclusters and isolated clusters. In Sect. 6 we analyse the sizes of voids defined by rich clusters from systems of various richness. In Sect. 7 we calculate the characteristic distance between the largest systems. In Sect. 8 we study the distribution of superclusters of different richness in void walls. Section 9 gives a summary of principal results.

We denote with h the Hubble constant in units of 100 km tex2html_wrap_inline1639 tex2html_wrap_inline1641.

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