伊藤 誠

With the help of a graph-theoretical approach, we have quantified two-dimensional galaxy distributions in observation and Cold Dark Matter (CDM) simulations. In our analysis, we adopted the Lyon-Meudon Extragalactic Database as a typical two-dimensional observation. To estimate adjacency matrices, we constructed constellation graphs from galaxy distributions, and calculated the distribution functions of the eigenvalues of these matrices. Using the mean absolute deviations, we compared the two-dimensional galaxy distributions in observations with CDM simulations in a statistical way. From our analysis we found that the CDM model with a density parameter of less than one is preferable to reproduce the galaxy distributions in the observations.

We use a graph theory for quantifying galaxy distributions in the cold dark matter (CDM) universe. Cosmological N-body simulations with CDM spectra are performed, and a constellation graph is constructed from these simulations. We apply graph theory to these constellation graphs and calculate the distribution functions of the eigenvalues of the adjacency matrices. In addition to a three-dimensional analysis, a two-dimensional analysis, an analysis in a slicelike geometry, and a redshift space analysis are also carried out. From our analyses, we find that the kurtosis and the average deviation of the distribution function of the eigenvalues are useful statistical measures for quantifying the galaxy distributions. We also find that the graph-theoretical approach possesses a discriminative ability with regard to the two-dimensional galaxy distributions. The slicelike geometry, which covers a rather narrow region of the sky, is not sufficient for the graph theoretical analysis. However, we find that the discriminative ability of the graph theory is recovered in redshift space.

We propose a graph-theoretical approach for quantifying the galaxy distributions in the universe. In order to examine the validity of this approach, we construct graphs based on our cosmological N-body simulations with scale-free power-lay spectra, and apply graph theory to them. constellation graph from our simulations, which is one of the most basic graphs. distribution function of the edge-length, order, degree, and the eigenvalue of the adjacency matrix of the constellation graph. From our analysis we find that the eigenvalue of the adjacency matrix is a good statistical measure for quantifying the galaxy distributions in a clear manner. For supplementary purposes we also construct a separated minimal spanning tree and a group graph, and examine the usefulness of the graph-theoretical approach.