A graph-theoretical approach for quantifying two-dimensional galaxy distributions and comparison with Cold Dark Matter universe

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