Related papers: Linear response theory for Google matrix
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…
On the case that the number of dangling nodes is large, PageRank computation can be proceeded with a much smaller matrix through lumping all dangling nodes of a web graph into a single node. Thus, it saves many computational cost and…
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…
There are several ideas being used today for Web information retrieval, and specifically in Web search engines. The PageRank algorithm is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied…
Using parallels with the quantum scattering theory, developed for processes in nuclear and mesoscopic physics and quantum chaos, we construct a reduced Google matrix $G_R$ which describes the properties and interactions of a certain subset…
Directed protein networks with only a few thousand of nodes are rather complex and do not allow to extract easily the effective influence of one protein to another taking into account all indirect pathways via the global network.…
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…
Node influence metrics have been applied to many applications, including ranking web pages on internet, or locations on spatial networks. PageRank is a popular and effective algorithm for estimating node influence. However, conventional…
PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of…
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…
The Google matrix is a positive, column-stochastic matrix that is used to compute the pagerank of all the web pages on the Internet: the eigenvector corresponding to the eigenvalue 1 is the pagerank vector. Due to its huge dimension, of the…
Since the advent of the Internet, quantifying the relative importance of web pages is at the core of search engine methods. According to one algorithm, PageRank, the worldwide web structure is represented by the Google matrix, whose…
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…
We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks.…
We apply the approach of the Google matrix, used in computer science and World Wide Web, to description of properties of neuronal networks. The Google matrix ${\bf G}$ is constructed on the basis of neuronal network of a brain model…
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…
The PageRank algorithm employed at Google assigns a measure of importance to each web page for rankings in search results. In our recent papers, we have proposed a distributed randomized approach for this algorithm, where web pages are…
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…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
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…