A Class of Random Matrices

The paper examines methods for assessing the distribution of elements in a stochastic matrix assuming the exponential distribution of elements in the corresponding adjacency matrix of a graph. Two cases are considered: the first assumes the homogeneity of all the graph vertices, while the second assumes the heterogeneity in the distribution of vertices with the corresponding density calculations. Hypothesis tests are formulated for the respective distributions to determine the membership of two graph vertices in the same cluster.