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In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…

Probability · Mathematics 2025-08-27 Antar Bandyopadhyay , Subhabrata Sen

We introduce tree linear cascades, a class of linear structural equation models for which the error variables are uncorrelated but need not be Gaussian nor independent. We show that, in spite of this weak assumption, the tree structure of…

Methodology · Statistics 2022-02-16 Nicholas C. Landolfi , Sanjay Lall

The study of the structural properties of large random planar graphs has become in recent years a field of intense research in computer science and discrete mathematics. Nowadays, a random planar graph is an important and challenging model…

Combinatorics · Mathematics 2009-07-15 Nikolaos Fountoulakis , Konstantinos Panagiotou

Uncover the vertices of a given graph, deterministic or random, in random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization…

Probability · Mathematics 2023-12-22 Svante Janson

A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…

Probability · Mathematics 2015-09-24 Maria Deijfen , Willemien Kets

Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…

We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…

Combinatorics · Mathematics 2024-07-29 Mikhail Isaev , Brendan D. McKay , Angus Southwell , Maksim Zhukovskii

Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…

Probability · Mathematics 2019-02-20 Jan Medina , Jorge Finke , Camilo Rocha

We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…

Statistical Mechanics · Physics 2011-11-16 E. Ben-Naim , P. L. Krapivsky

A covariance graph is an undirected graph associated with a multivariate probability distribution of a given random vector where each vertex represents each of the different components of the random vector and where the absence of an edge…

Probability · Mathematics 2009-12-15 Dhafer Malouche , Bala Rajaratnam

We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…

Disordered Systems and Neural Networks · Physics 2015-05-28 Hendrike Klein-Hennig , Alexander K. Hartmann

Bilateral agreement based random undirected graphs were introduced and analyzed by La and Kabkab in 2015. The construction of the graph with $n$ vertices in this model uses a (random) preference order on other $n-1$ vertices and each vertex…

Probability · Mathematics 2025-07-09 Hossein Dabirian , Vijay Subramanian

We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…

Combinatorics · Mathematics 2007-05-23 Nikolaos Fountoulakis

Monadic second order logic can be used to express many classical notions of sets of vertices of a graph as for instance: dominating sets, induced matchings, perfect codes, independent sets or irredundant sets. Bounds on the number of sets…

Discrete Mathematics · Computer Science 2020-05-08 Matthieu Rosenfeld

We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…

Soft Condensed Matter · Physics 2007-05-23 Bo Soderberg

We consider a setting where multiple entities inter-act with each other over time and the time-varying statuses of the entities are represented as multiple correlated time series. For example, speed sensors are deployed in different…

Machine Learning · Computer Science 2021-03-23 Razvan-Gabriel Cirstea , Chenjuan Guo , Bin Yang

This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all…

Machine Learning · Statistics 2014-04-15 Divyanshu Vats , Robert D. Nowak , Richard G. Baraniuk

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…

Probability · Mathematics 2014-10-22 Sébastien Bubeck , Ronen Eldan , Elchanan Mossel , Miklós Z. Rácz

We consider the process of uncovering the vertices of a random labeled tree according to their labels. First, a labeled tree with $n$ vertices is generated uniformly at random. Thereafter, the vertices are uncovered one by one, in order of…

Probability · Mathematics 2023-01-03 Benjamin Hackl , Alois Panholzer , Stephan Wagner

We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…

Combinatorics · Mathematics 2024-05-07 Colin McDiarmid