Network analysis of the COSMOS galaxy field

Abstract

The galaxy data provided by COSMOS survey for 1 • × 1 • field of sky are analysed by methods of complex networks. Three galaxy samples (slices) with redshifts ranging within intervals 0.88÷0.91, 0.91÷0.94 and 0.94÷0.97 are studied as two-dimensional projections for the spatial distributions of galaxies. We construct networks and calculate network measures for each sample, in order to analyse the network similarity of different samples, distinguish various topological environments, and find associations between galaxy properties (colour index and stellar mass) and their topological environments.Results indicate a high level of similarity between geometry and topology for different galaxy samples and no clear evidence of evolutionary trends in network measures. The distribution of local clustering coefficient C manifests three modes which allow for discrimination between stand-alone singlets and dumbbells (0 ≤ C ≤ 0.1), intermediately packed (0.1 < C < 0.9) and clique (0.9 ≤ C ≤ 1) like galaxies.Analysing astrophysical properties of galaxies (colour index and stellar masses), we show that distributions are similar in all slices, however weak evolutionary trends can also be seen across redshift slices. To specify different topological environments we have extracted selections of galaxies from each sample according to different modes of C distribution. We have found statistically significant associations between evolutionary parameters of galaxies and selections of C: the distribution of stellar mass for galaxies with interim C differ from the corresponding distributions for stand-alone and clique galaxies, and this difference holds for all redshift slices. The colour index realises somewhat different behaviour.

Large-scale structures in the ΛCDM Universe: network analysis and machine learning

“…However, in our opinion, the crucial parameters are average values of metrics, degree k and clustering coefficient Cl (definitions are given in the next section) in particular. These values at l = 2 h −1 Mpc are close to ones computed in de Regt et al (2018) in their network analysis, k = 6.77, Cl = 0.603 (see the Table 1 for average values we obtained in our networks). Therefore, we conclude that chosen value is appropriate to study the Cosmic Web we consider.…”

“…degree, Katz centrality, triangles), those that have similar distributions in different subpopulations (closeness centrality, clustering coefficient, square clustering coefficient), and those that are somewhere in the middle between previous two groups, having somewhat different distributions (harmonic, eigenvector, betweenness centralities). Distributions of degree and clustering coefficient we obtained have comparable distribution with those in (de Regt et al 2018). It is also interesting to point out that clustering coefficient seems to have distribution, indifferent to type of topology structure, while it was shown in (de Regt et al 2018) that distributions of the color index and stellar mass of galaxies as nodes are different for populations with different clustering coefficient.…”

“…As it has been noted before (Hong & Dey 2015;de Regt et al 2018), network linking length affects all the numbers, relations and laws one may discover when exploring the network. Indeed, having linking length too small will result in the disconnected network and reveal no structures in the web, while having it too large will not show the peculiarities and important nodes of the network.…”

“…All of them were computed with the help of NetworkX package for Python. These metrics are widely used when studying social networks (Brandes 2001), transport (Berche et al 2012), communications and other kind of networks (Albert & Barabasi 2002), including Cosmic Web (de Regt et al 2018). On the other hand, it occurs that adding more metrics of the node doesn't help in ML problem of predicting the topology.…”

“…The pioneering work of this approach in cosmology (Hong & Dey 2015) addressed the problem of relation between network centralities of nodes in the Cosmic Web and the type of topological population of the corresponding galaxy. The following papers studied different usages of complex networks analysis of the Cosmic Web: discriminat-E-mail: maksym.tsizh@lnu.edu.ua ing of different topologies in population with similar twopoint correlation functions (Hong 2016), discovering various ways of network construction (Coutinho et al 2016), finding similarity and peculiarity of physical galaxy properties (color, brightness, mass index) of different topology (defined by network characteristic) environment population (de Regt et al 2018), relating correlation function and relative size of the largest connected component of network Zhang et al (2018), studying connectivity of Gaussian Random Fieldlike galaxy field (Codis et al 2018) as a probe of evolution of structures and the nature of dark energy. In recent works, (Hong et al 2019a) and (Hong et al 2019b), authors study how the transitivity of the Cosmic Web and its other network characteristic can distinguish models of dark energy in cosmological simulations and different scenarios of Lyalpha emitters.…”