We consider the Buckley-Osthus implementation of preferential attachment and its ability to model the web host graph in two aspects. One is the degree distribution that we observe to follow the power law, as often being the case for real-world graphs. Another one is the two-dimensional edge distribution, the number of edges between vertices of given degrees. We fit a single "initial attractiveness" parameter a of the model, first with respect to the degree distribution of the web host graph, and then, absolutely independently, with respect to the edge distribution. Surprisingly, the values of a we obtain turn out to be nearly the same. Therefore the same model with the same value of the parameter a fits very well the two independent and basic aspects of the web host graph. In addition, we demonstrate that other models completely lack the asymptotic behavior of the edge distribution of the web host graph, even when accurately capturing the degree distribution.To the best of our knowledge, this is the first study confirming the ability of preferential attachment models to reflect the distribution of edges between vertices with respect to their degrees in a real graph of Internet.

No abstract

No abstract

Traditional link-based web ranking algorithms run on a single web snapshot without concern of the dynamics of web pages and links. In particular, the correlation of web pages freshness and their classic PageRank is negative (see [11]). For this reason, in recent years a number of authors introduce some algorithms of PageRank actualization. We introduce our new algorithm called Actual PageRank, which generalizes some previous approaches and therefore provides better capability for capturing the dynamics of the Web. To the best of our knowledge we are the first to conduct ranking evaluations of a fresh-aware variation of PageRank on a large data set. The results demonstrate that our method achieves more relevant and fresh results than both classic PageRank and its "fresh" modifications.

No abstract