The fast finding of most influential nodes in a network graph and its declustering constitute important research problems of the analysis of Web communication, social and complex networks. PageRank \cite{Vol:10} and a Max-linear model \cite{GisKlu:15} are considered as two indices of the influence of network nodes. An extremal index of PageRank determines the first hitting time, i.e. a minimal time to reach the first influential node by means of a PageRank random walk. Following \cite{Jel:10}, \cite{Vol:10}, we consider the PageRank of a random Web page as an autoregressive process with a random number of random coefficients that depend on ranks of incoming nodes and their out-degrees, and a user preference term. The coefficients are assumed to be %independent and regularly varying distributed with different tail indices. It is proved that the tail and extremal indices are the same for both PageRank and the Max-linear model and the values of the extremal index depending on the tail indices are found \cite{Markovich}. The results are based on the study of stochastic sequences of random lengths \cite{Gold:13} and the comparison of the distributions of their maxima and linear combinations. The exposition is accompanied by some examples based on simulation and the analysis of graph data stemming from real Web graphs.

The evaluation at integer arguments of the Riemann's zeta function and of some other Dirichlet series is presented. Using elementary analytic techniques and summation formulas applied to the Bernoulli polynomials formulas for sums of some divergent series of zeta functions are also derived.