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This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…

Probability · Mathematics 2019-07-02 Roy Cerqueti , Emilio De Santis

Graph neural networks (GNNs), which propagate the node features through the edges and learn how to transform the aggregated features under label supervision, have achieved great success in supervised feature extraction for both node-level…

Machine Learning · Statistics 2022-11-01 Yilin He , Chaojie Wang , Hao Zhang , Bo Chen , Mingyuan Zhou

Networks arising from social, technological and natural domains exhibit rich connectivity patterns and nodes in such networks are often labeled with attributes or features. We address the question of modeling the structure of networks where…

Social and Information Networks · Computer Science 2011-06-28 Myunghwan Kim , Jure Leskovec

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…

Physics and Society · Physics 2021-04-07 Giulia Bertagnolli , Manlio De Domenico

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…

Social and Information Networks · Computer Science 2018-05-02 Xiao Zhang , Cristopher Moore , M. E. J. Newman

Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…

Probability · Mathematics 2015-04-29 Sidney Resnick , Gennady Samorodnitsky

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…

Disordered Systems and Neural Networks · Physics 2009-11-10 Marian Boguna , Romualdo Pastor-Satorras

Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…

Machine Learning · Computer Science 2022-08-23 Peter Belcak , Roger Wattenhofer

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…

Probability · Mathematics 2022-09-30 Ercan Sönmez , Arnaud Rousselle

In this paper we introduce a new simple but powerful general technique for the study of edge- and vertex-reinforced processes with super-linear reinforcement, based on the use of order statistics for the number of edge, respectively of…

Probability · Mathematics 2016-06-03 Codina Cotar , Debleena Thacker

Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…

Discrete Mathematics · Computer Science 2018-03-30 Jan Dreier , Philipp Kuinke , Peter Rossmanith

Couplings play a central role in contemporary Markov chain Monte Carlo methods and in the analysis of their convergence to stationarity. In most cases, a coupling must induce relatively fast meeting between chains to ensure good…

Methodology · Statistics 2021-02-04 John O'Leary

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

Machine Learning · Computer Science 2022-05-11 Jurijs Nazarovs , Ronak R. Mehta , Vishnu Suresh Lokhande , Vikas Singh

We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…

Probability · Mathematics 2019-11-19 Yury Malyshkin

Statistical inference in evolutionary models with site-dependence is a long-standing challenge in phylogenetics and computational biology. We consider the problem of approximating marginal sequence likelihoods under dependent-site models of…

Computation · Statistics 2025-11-12 Joseph Mathews , Scott C. Schmidler

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…

Probability · Mathematics 2011-08-31 Sourav Chatterjee , Persi Diaconis , Allan Sly

A large number and diversity of techniques have been offered in the literature in recent years for solving multi-label classification tasks, including classifier chains where predictions are cascaded to other models as additional features.…

Machine Learning · Computer Science 2019-07-19 Jesse Read , Luca Martino

We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…

Probability · Mathematics 2019-01-09 Caio Alves , Rodrigo Ribeiro , Remy Sanchis

Many widely used network centralities are based on counting walks that meet specific criteria. This paper introduces a systematic framework for walk enumeration using generating functions. We introduce a first-passage decomposition that…

Theoretical Economics · Economics 2025-08-14 Yang Sun , Wei Zhao , Junjie Zhou

Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…

Probability · Mathematics 2009-10-05 Lorenz A. Gilch , Sebastian Müller