Related papers: PageRank's behavior under degree-degree correlatio…
The article deals with two classes of growing random graphs following the preferential attachment rule with a linear weight function, L-graphs, and hybrid Pennock graphs. We determine the exact final vertex degree distribution and the exact…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
We investigate the consensus dynamics of the voter model on large random graphs with heterogeneous and directed features, focusing in particular on networks with power-law degree distributions. By extending recent results on sparse directed…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
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…
In this paper, we investigate the potential of the age-dependent random connection model (ADRCM) with the aim of representing higher-order networks. A key contribution of our work are probabilistic limit results in large domains. More…
We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition…
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 identify the asymptotic distribution of $p$-rank of the sandpile group of a random directed bipartite graphs which are not too imbalanced. We show this matches exactly that of the Erd{\"o}s-R{\'e}nyi random directed graph model,…
Despite great effort spent measuring topological features of large networks like the Internet, it was recently argued that sampling based on taking paths through the network (e.g., traceroutes) introduces a fundamental bias in the observed…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
PageRank is a ranking of the web pages that measures how often a given web page is visited by a random surfer on the web graph, for a simple model of web surfing. It seems realistic that PageRank may also have an influence on the behavior…
This paper develops a generalization of the PageRank model of page centralities in the global webgraph of hyperlinks. The webgraph of adjacencies is generalized to a valued directed graph, and the scalar dampening coefficient for walks…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
In this paper, we consider a problem of learning supervised PageRank models, which can account for some properties not considered by classical approaches such as the classical PageRank algorithm. Due to huge hidden dimension of the…
Geometric scale-free random graphs are popular models for networks that exhibit as heavy-tailed degree distributions, small-worldness and high clustering. In these models, vertices have weights that cause the heavy-tailed degrees and are…
We consider a random model for directed graphs whereby an arc is placed from one vertex to another with a prescribed probability which may vary from arc to arc. Using perturbation bounds as well as Chernoff inequalities, we show that the…
The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…