A graph-theoretical approach for comparison of observational galaxy distributions with cosmological N-body simulations

¹ Faculty of Education and Human Studies, Akita University, 1-1 Tegata-gakuen, Akita-shi, Akita 010-8502, Japan
² National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka-shi Tokyo 181-8588, Japan e-mail: takeuchi@optik.mtk.nao.ac.jp
³ Faculty of Economics and Information, Gifu Shotoku Gakuen University, 1-38 Nakauzura, Gifu-shi, Gifu, 500-8288, Japan e-mail: mitoh@gifu.shotoku.ac.jp


Corresponding author: H. Ueda, ueda@ipc.akita-u.ac.jp

Received: 8 January 2002
Accepted: 4 November 2002

Abstract

Using a graph-theoretical approach, we compared the galaxy distributions in a flux-limited galaxy sample extracted from the Lyon-Meudon Extragalactic Database (“the LEDA subsample”) with those in cosmological N-body simulations. To derive information on the density parameter of our Universe, we used CDM simulations with (, , 0.9), (0.5, 0.5), (1.0, 0.0), and prepared artificial samples. Constellation graphs were constructed from the galaxy distributions in the LEDA subsample and those in these artificial samples, and graph theory was applied. For statistical comparison, the mean absolute deviations of the distribution functions of the eigenvalues of the adjacency matrices were calculated. From our analysis we found that a low-density parameter is preferable, although the LEDA subsample we used in this study is not deep enough to provide a definite estimate of the cosmological parameter set of the Universe.