Related papers: Personalized PageRank dimensionality and algorithm…
Real-world graphs grow rapidly with edge and vertex insertions over time, motivating the problem of efficiently maintaining robust node representation over evolving graphs. Recent efficient GNNs are designed to decouple recursive message…
Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged in learning problems. While most of the existing literature…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
Finding dense subgraphs of a large network is a fundamental problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications over the last five decades. However, most existing…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
Personalized recommendations form an important part of today's internet ecosystem, helping artists and creators to reach interested users, and helping users to discover new and engaging content. However, many users today are skeptical of…
PageRank is a well-known centrality measure for the web used in search engines, representing the importance of each web page. In this paper, we follow the line of recent research on the development of distributed algorithms for computation…
Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their…
We analyse a mean-field model of Personalized PageRank on the Erdos-Renyi random graph containing a denser planted Erdos-Renyi subgraph. We investigate the regimes where the values of Personalized PageRank concentrate around the mean-field…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning. In this paper, we study PageRank in undirected random graphs with an expansion property. The Chung-Lu random graph is…
To rank nodes in quasi-hierarchical networks of social nature, it is necessary to carry out a detailed analysis of the network and evaluate the results obtained according to all the given criteria and identify the most influential nodes.…
The push algorithm was proposed first by Jeh and Widom in the context of personalized PageRank computations (albeit the name "push algorithm" was actually used by Andersen, Chung and Lang in a subsequent paper). In this note we describe the…
Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured…
The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank function along with persistent homology to obtain a scalable…
Modern recommender systems model people and items by discovering or `teasing apart' the underlying dimensions that encode the properties of items and users' preferences toward them. Critically, such dimensions are uncovered based on user…
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This…
We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an $m$-dimensional metric space with power-law distributed…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
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…