47094

Автор(ов): 

1

Параметры публикации
Тип публикации: 
Тезисы доклада
Название: 
Extremes of stochastic sequences with application to web graphs
Наименование конференции: 
12th International Vilnius Conference on Probability Theory and Mathematical Statistics and 2018 IMS Annual Meeting on Probability and Statistics
Наименование источника: 
Proceedings of the 12th International Vilnius Conference on Probability Theory and Mathematical Statistics
Город: 
Вильнюс
Издательство: 
Вильнюсский университет
Год издания: 
2018
Страницы: 
266
Аннотация
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 %tail and with different tail indices. %the same tail index 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.
Библиографическая ссылка: 
Маркович Н.М. Extremes of stochastic sequences with application to web graphs / Proceedings of the 12th International Vilnius Conference on Probability Theory and Mathematical Statistics. Вильнюс: Вильнюсский университет, 2018. С. 266.