Analysis of clustering coefficients of online social networks by duplication models

In this paper we propose to model the formation of online social networks by a duplication model. In this model vertices are added into the network one at a time. Each vertex is first attached to a randomly selected vertex. Each neighbor of the attached vertex establishes an edge with the new vertex with a probability. A main contribution of this paper is that we derive analytically the clustering coefficient for this model. Numerical studies show that the range of mean degree and the clustering coefficient of the duplication model is quite large. By properly choosing values for the parameters of our model, the mean degree and the clustering coefficient match well with those of popular online social networks.