Abstract <p>This paper presents the results of numerical simulation of nearest neighbor graphs (NNGs) generated by random distance matrices. Both symmetric and nonsymmetric random matrices are considered. Empirical distributions of graphs by the number of connected fragments, fragments by the number of vertices, and vertices by degrees are investigated. The obtained statistics are considered as a&#xa0;benchmark for a new approach used to estimate the probability of the dependence of the sample data. Since the benchmark does not depend on the distribution function of the elements of random matrices, it becomes possible to tabulate a nonparametric statistical criterion for the dependence of random elements of the sample on the probability of implementing the structure of the NNG generated by this sample. The statistics found also make it possible to compare various pseudo-random number generators and some natural generators. This paper provides an example with the analysis of graphs generated by the decimal representation of the number pi and shows that the first 50 billion digits of this record are not independent random variables.</p>