Related papers: Local weak convergence for PageRank
We present a comprehensive analysis of algebraic methods for controlling the stationary distribution of PageRank-like random walkers. Building upon existing literature, we compile and extend results regarding both structural control…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
We investigate several geometric models of network which simultaneously have some nice global properties, that the small diameter property, the small-community phenomenon, which is defined to capture the common experience that (almost)…
This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
The World-Wide Web (WWW) is characterized by a strong community structure in which communities of webpages (e.g. those sharing a common keyword) are densely interconnected by hyperlinks. We study how such network architecture affects the…
Many systems, including the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example…
We study the spread of influence in a social network based on the Linear Threshold model. We derive an analytical expression for evaluating the expected size of the eventual influenced set for a given initial set, using the probability of…
In the paper we investigate power law for PageRank components for the Buckley-Osthus model for web graph. We compare different numerical methods for PageRank calculation. With the best method we do a lot of numerical experiments. These…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
Complex networks are graphs representing real-life systems that exhibit unique characteristics not found in purely regular or completely random graphs. The study of such systems is vital but challenging due to the complexity of the…
Finding pertinent information is not limited to search engines. Online communities can amplify the influence of a small number of power users for the benefit of all other users. Users' information foraging in depth and breadth can be…
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…
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…
In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…
We compare two link analysis ranking methods of web pages in a site. The first, called Site Rank, is an adaptation of PageRank to the granularity of a web site and the second, called Popularity Rank, is based on the frequencies of user…
Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale behavior, it is typically assumed, without a clear statement,…
Word and graph embeddings are widely used in deep learning applications. We present a data structure that captures inherent hierarchical properties from an unordered flat embedding space, particularly a sense of direction between pairs of…
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…