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We study the localization properties of eigenvectors of the Google matrix, generated both from the World Wide Web and from the Albert-Barabasi model of networks. We establish the emergence of a delocalization phase for the PageRank vector…

We develop the linear response theory for the Google matrix PageRank algorithm with respect to a general weak perturbation and a numerical efficient and accurate algorithm, called LIRGOMAX algorithm, to compute the linear response of the…

In this paper we have modified the existing page ranking mechanism as an advanced Page Rank Algorithm based on Semantics Inlinks Outlinks and Google Analytics. We have used Semantics page ranking to rank pages according to the word searched…

The choice of the PageRank damping factor is not evident. The Google's choice for the value c=0.85 was a compromise between the true reflection of the Web structure and numerical efficiency. However, the Markov random walk on the original…

We study the statistical properties of spectrum and eigenstates of the Google matrix of the citation network of Physical Review for the period 1893 - 2009. The main fraction of complex eigenvalues with largest modulus is determined…

We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method we analyze the distribution of eigenvalues in the complex…

Social networks have ensured the expanding disproportion between the face of WWW stored traditionally in search engine repositories and the actual ever changing face of Web. Exponential growth of web users and the ease with which they can…

We give a new link spam detection and PageRank demotion algorithm called MaxRank. Like TrustRank and AntiTrustRank, it starts with a seed of hand-picked trusted and spam pages. We define the MaxRank of a page as the frequency of visit of…

PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible…

We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure…

This paper shows that pairwise PageRank orders emerge from two-hop walks. The main tool used here refers to a specially designed sign-mirror function and a parameter curve, whose low-order derivative information implies pairwise PageRank…

Recommendations are central to the utility of many websites including YouTube, Quora as well as popular e-commerce stores. Such sites typically contain a set of recommendations on every product page that enables visitors to easily navigate…

A typical web search engine consists of three principal parts: crawling engine, indexing engine, and searching engine. The present work aims to optimize the performance of the crawling engine. The crawling engine finds new web pages and…

In this paper, we consider a problem of learning supervised PageRank models, which can account for some properties not considered by classical approaches such as the classical PageRank algorithm. Due to huge hidden dimension of the…

The Internet is one of the most valuable technologies invented to date. Among them, Google is the most widely used search engine. The PageRank algorithm is the backbone of Google search, ranking web pages according to relevance and recency.…

Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the…

The WorldWideWeb (WWW) is a huge conservatory of web pages. Search Engines are key applications that fetch web pages for the user query. In the current generation web architecture, search engines treat keywords provided by the user as…

The WorldWide Web is one of the most important communication systems we use in our everyday life. Despite its central role, the growth and the development of the WWW is not controlled by any central authority. This situation has created a…

Development of efficient business process models and determination of their characteristic properties are subject of intense interdisciplinary research. Here, we consider a business process model as a directed graph. Its nodes correspond to…

A fundamental problem arising in many applications in Web science and social network analysis is, given an arbitrary approximation factor $c>1$, to output a set $S$ of nodes that with high probability contains all nodes of PageRank at least…