An average distance in the power-law configuration graphs

In random configuration graphs with a discrete power-law vertex degree distribution with a fixed parameter, the average distance in the graph is considered, i. e., the arithmetic mean of distances between all pairs of graph nodes. This characteristic is estimated using simulation methods. Due to computational constraints, the author considers graphs in the pre-asymptotic domain (in this paper, these are the graphs up to 7000 nodes). The models of dependencies of the average distance on the graph size and the parameter of vertex degree distribution are reseived. The obtained results are compared with the results of theoretical studies of the typical distance in a graph in the asymptotics (i. e., when the number of graph vertices tends to infinity), given in the works by R. Hofstad.