Clustering Coefficient of a Spatial Preferential Attachment Model

Abstract

The clustering structure of a graph in a spatial preferential attachment model whose similarity to real-world networks has been shown in many aspects is considered. The behavior of the local clustering coefficient is studied. Namely, the asymptotic behavior of its average value over all graph vertices of a certain degree as the graph size tends to infinity is examined. This characteristic has not been previously analyzed in the SPA model, and it reflects the typical dependence of the clustering structure near some vertex on its degree in the graph. Additionally, it is shown that, with a high probability, there is a vertex for which the value of the clustering coefficient differs from its average.