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We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…
The galaxies of nonstandard enlargements of conventionally infinite as well as of transfinite graphs are defined, analyzed, and illustrated by some examples. It is then shown that any such enlargement either has exactly one galaxy, its…
Filaments of galaxies are known to stretch between galaxy clusters at all redshifts in a complex manner. In this Letter, we present an analysis of the frequency and distribution of inter-cluster galaxy filaments selected from the 2dF Galaxy…
The theory of galaxy formation posits a clear correlation between the spin of galaxies and the orientation of the elements of the large-scale structure of the Universe, particularly cosmic filaments. A substantial number of observational…
The matter distribution around galaxy clusters is distributed over several filaments, reflecting their positions as nodes in the large-scale cosmic web. The number of filaments connected to a cluster, namely its connectivity, is expected to…
We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the…
The cosmic web is the largest scale manifestation of the anisotropic gravitational collapse of matter. It represents the transitional stage between linear and non-linear structures and contains easily accessible information about the early…
Multi-connected Universe models with space idenfication scales smaller than the size of the observable universe produce topological images in the catalogs of cosmic sources. In this review, we present the recent developments for the search…
I review recent progress in the study of the large-scale structure of the Universe through the distribution of clusters of galaxies, concentrating on new results using X-ray selected samples. After discussing the importance of understanding…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
Many approaches to obtaining cosmological constraints rely on the connection between galaxies and dark matter. However, the distribution of galaxies is dependent on their formation and evolution as well as the cosmological model, and galaxy…
Cosmic filaments are the main transport channels of matter in the Megaparsec universe, and represent the most prominent structural feature in the matter and galaxy distribution. Here we describe and define the physical and dynamical nature…
We review one of the most fruitful areas in cosmology today that bridge theory and data - the temporal growth of large-scale structure. We go over the growth's physical foundations, and derive its behavior in simple cosmological models.…
Using a population of large-scale filaments extracted from an AREPO simulation of a Milky Way-like galaxy, we seek to understand the extent to which observed large-scale filament properties (with lengths $\gtrsim 100$ pc) can be explained…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
Gravitational-collapse-based explanations of the cosmic web lead to problems in estimating the total mass in the universe. A first-principles several-scales model is developed here for the structural organisation of cosmic matter in a flat…
While galaxy cluster catalogs were compiled many decades ago, other structural elements of cosmic web are detected at definite level only in the newest works. For example, extragalactic filaments were described by velocity field and SDSS…
We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed degrees. For rank-one inhomogeneous random graphs, such…
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…
The field of astronomy is experiencing a data explosion driven by significant advances in observational instrumentation, and classical methods often fall short of addressing the complexity of modern astronomical datasets. Probabilistic…