Related papers: PageRank in undirected random graphs
Personalized PageRank is an algorithm to classify the improtance of web pages on a user-dependent basis. We introduce two generalizations of Personalized PageRank with node-dependent restart. The first generalization is based on the…
Given an undirected graph $G=(V, E)$, the Personalized PageRank (PPR) of $t\in V$ with respect to $s\in V$, denoted $\pi(s,t)$, is the probability that an $\alpha$-discounted random walk starting at $s$ terminates at $t$. We study the time…
There has been a rising interest in graph neural networks (GNNs) for representation learning over the past few years. GNNs provide a general and efficient framework to learn from graph-structured data. However, GNNs typically only use the…
The significance of the PageRank algorithm in shaping the modern Internet cannot be overstated, and its Complex Network theory foundations continue to be a subject of research. In this article we carry out a systematic study of the…
Regarding the analysis of Web communication, social and complex networks the fast finding of most influential nodes in a network graph constitutes an important research problem. We use two indices of the influence of those nodes, namely,…
PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the…
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 importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts - including ranking websites - and can be interpreted as the average portion of time spent at…
We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…
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 spectral radius of the adjacency matrix can impact both algorithmic efficiency as well as the stability of solutions to an underlying dynamical process. Although much research has considered the distribution of the spectral radius for…
Recently bipartite graphs have been widely used to represent the relationship two sets of items for information retrieval applications. The Web offers a wide range of data which can be represented by bipartite graphs, such us movies and…
In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal…
The PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that the PageRank obeys a `power law' with the same exponent as the In-Degree. This paper presents a novel mathematical model that explains this…
The PageRank algorithm is used to rank web pages by their importance. Since its development, the PageRank algorithm is a critical and fundamental part of search engines today. PageRank is a graph-based algorithm that ranks pages based on…
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,…
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…
PageRank is a well-known algorithm whose robustness helps set a standard benchmark when processing graphs and analytical problems. The PageRank algorithm serves as a standard for many graph analytics and a foundation for extracting graph…
While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major leagues to…
The PageRank algorithm employed by Google quantifies the importance of each page by the link structure of the web. To reduce the computational burden the distributed randomized PageRank algorithms (DRPA) recently appeared in literature…