Analysis of Vertex Degree Distributions in Preferential Attachment Graphs with Power Weight Function

Abstract

Preferential attachment graphs with power weight function are considered in the paper. The dependence of vertex degree distributions in the graphs on the weight function parameter is analyzed. The purpose of the analysis is to identify such ranges of the parameter values that cause the homogeneous (within the ranges) types of vertex degree distributions, and to determine the asymptotic properties of these distributions. The paper shows the effectiveness of the approach used for the first time. The approach combines the application of found by the authors exact recurrence formulas of the investigated distributions with approximate explicit expressions of the distributions. The application of obtained results and the approach developed in the study makes it possible to increase the adequacy of modeling of growing networks, whose properties, as is well known, depend significantly on the asymptotic behavior of vertex degree distribution.