Related papers: PageRank of integers
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
The existing search engines sometimes give unsatisfactory search result for lack of any categorization of search result. If there is some means to know the preference of user about the search result and rank pages according to that…
In the light of the need to achieve a ranking which is understood by all tennis supporters, the ATP ranking is exposed to constant complaints from players and at the same time exposes new players to be benefited with a good tournament to be…
Ranking algorithms are the information gatekeepers of the Internet era. We develop a stylized model to study the effects of ranking algorithms on opinion dynamics. We consider a search engine that uses an algorithm based on popularity and…
Typing Yesterday into the search-bar of your browser provides a long list of websites with, in top places, a link to a video by The Beatles. The order your browser shows its search results is a notable example of the use of network…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
The inference of rankings plays a central role in the theory of social choice, which seeks to establish preferences from collectively generated data, such as pairwise comparisons. Examples include political elections, ranking athletes based…
A nonlinear generalisation of the PageRank problem involving the Moore-Penrose inverse of an incidence matrix is developed for local graph partitioning purposes. The Levenberg-Marquardt method with a full rank Jacobian variant provides a…
We apply the Google PageRank algorithm to assess the relative importance of all publications in the Physical Review family of journals from 1893--2003. While the Google number and the number of citations for each publication are positively…
Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected…
Internet Protocol (IP) addresses are frequently used as a method of locating web users by researchers in several different fields. However, there are competing reports concerning the accuracy of those locations, and little research has been…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
We present new algorithms for Personalized PageRank estimation and Personalized PageRank search. First, for the problem of estimating Personalized PageRank (PPR) from a source distribution to a target node, we present a new bidirectional…
We describe a new method of reduced Google matrix which allows to establish direct and hidden links between a subset of nodes of a large directed network. This approach uses parallels with quantum scattering theory, developed for processes…
In order to protect an image search engine's users from undesirable results adult images' classifier should be built. The information about links from websites to images is employed to create such a classifier. These links are represented…
Inspired by Pythagoras's belief that numbers are the absolute reality, we obtain some demonstrational results about topological properties of integer networks, in which the vertices represent integers and two vertices are neighbors if and…
A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each…
The data structure at the core of large-scale search engines is the inverted index, which is essentially a collection of sorted integer sequences called inverted lists. Because of the many documents indexed by such engines and stringent…
In a prime number decomposition of integers in a given set, the occurrence frequencies of prime numbers are shown to satisfy a general forms of Zipf's law.
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…