Related papers: PageRank in undirected random graphs
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…
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…
Seeded PageRank is an important network analysis tool for identifying and studying regions nearby a given set of nodes, which are called seeds. The seeded PageRank vector is the stationary distribution of a random walk that randomly resets…
We present new algorithms for Personalized PageRank estimation and Personalized PageRank search. First, for the problem of estimating Personalized PageRank (PPR) from a source distribution to a target node, we present a new bidirectional…
{\it SimRank} is a classic measure of the similarities of nodes in a graph. Given a node $u$ in graph $G =(V, E)$, a {\em single-source SimRank query} returns the SimRank similarities $s(u, v)$ between node $u$ and each node $v \in V$. This…
Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of…
For any fixed integer $R \geq 2$ we characterise the typical structure of undirected graphs with vertices $1, ..., n$ and maximum degree $R$, as $n$ tends to infinity. The information is used to prove that such graphs satisfy a labelled…
In this paper we present a novel algorithm to study the evolution of credit risk across complex multilayer networks. Pagerank-like algorithms allow for the propagation of an influence variable across single networks, and allow quantifying…
In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…
Personalized PageRank (PPR) is a traditional measure for node proximity on large graphs. For a pair of nodes $s$ and $t$, the PPR value $\pi_s(t)$ equals the probability that an $\alpha$-discounted random walk from $s$ terminates at $t$ and…
When we search online for content, we are constantly exposed to rankings. For example, web search results are presented as a ranking, and online bookstores often show us lists of best-selling books. While popularity-based ranking algorithms…
In a former paper we simplified the proof of a theorem on personalized random walk that is fundamental to graph nodes clustering and generalized it to bipartite graphs for a specific case where the proobability of random jump was…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
This paper systematically studies the behavior of the leading eigenvectors for independent edge undirected random graphs generated from a general latent position model whose link function is possibly infinite rank and also possibly…
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…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
In evaluating an algorithm, worst-case analysis can be overly pessimistic. Average-case analysis can be overly optimistic. An intermediate approach is to show that an algorithm does well on a broad class of input distributions. Koutsoupias…
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…
Popular graph neural networks are shallow models, despite the success of very deep architectures in other application domains of deep learning. This reduces the modeling capacity and leaves models unable to capture long-range relationships.…