Related papers: Towards two-dimensional search engines
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…
Nowadays, information describing navigation behaviour of internet users are used in several fields, e-commerce, economy, sociology and data science. Such information can be extracted from different knowledge bases, including…
We construct the Google matrix of the entire Twitter network, dated by July 2009, and analyze its spectrum and eigenstate properties including the PageRank and CheiRank vectors and 2DRanking of all nodes. Our studies show much stronger…
We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003 - 2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank…
We study the structural properties of the neural network of the C.elegans (worm) from a directed graph point of view. The Google matrix analysis is used to characterize the neuron connectivity structure and node classifications are…
The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval…
We build up a directed network tracing links from a given integer to its divisors and analyze the properties of the Google matrix of this network. The PageRank vector of this matrix is computed numerically and it is shown that its…
PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability…
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…
The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special…
In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank…
Google's PageRank method was developed to evaluate the importance of web-pages via their link structure. The mathematics of PageRank, however, are entirely general and apply to any graph or network in any domain. Thus, PageRank is now…
The search engine is tightly coupled with social networks and is primarily designed for users to acquire interested information. Specifically, the search engine assists the information dissemination for social networks, i.e., enabling users…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social…
The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the…
Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the…
Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world…
In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized…
The bipartite graph is a ubiquitous data structure that can model the relationship between two entity types: for instance, users and items, queries and webpages. In this paper, we study the problem of ranking vertices of a bipartite graph,…