  In this paper we present new improvement ideas of the original PageRank
algorithm. The first idea is to introduce an evaluation of the statistical
reliability of the ranking score of each node based on the local graph property
and the second one is to introduce the notion of the path diversity. The path
diversity can be exploited to dynamically modify the increment value of each
node in the random surfer model or to dynamically adapt the damping factor. We
illustrate the impact of such modifications through examples and simple
simulations.
