Minimum and maximum of the average distance in power-law configuration graphs

Abstract

The article studies configuration graphs with a discrete fixed-parameter power-law distribution of node degrees. Simulation is applied to estimate the average distance (the arithmetic mean of all distances between all pairs of graph vertices), and two characteristics are considered: the minimum and the maximum average distance in the graph. The dependences of these characteristics on the graph size and the vertex degree distribution parameter are obtained and the empirical confidence interval of the average distance in the power-law configuration graph is constructed