The PageRank Vector of a Scale-Free Web Network Growing by Preferential Attachment.

We consider a scale-free model of the Web network that is evolving by preferential attachment schemes and derive an explicit formula of its PageRank vector. Its i th element indicates the probability that a surfer resides at a related Web page i in a stationary regime of an associated random walk. Considering the growth of a directed Web graph, we apply linear preferential attachment schemes proposed by Samorodnitsky et al. (2016). To express the probability of a connection between two nodes of this Web graph, our derivation allows us to avoid the consideration of complicated paths with random lengths and to cover both self-loops and multiple edges between nodes. An algorithm of the PageRank vector calculation for graphs without loops is provided. The approach can be extended in a similar way to graphs with loops. In this way, our approach enhances existing analysis schemes. It provides a better insight on the PageRank of growing scale-free Web networks and supports the adaptation of the model to gathered network statistics.