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Related papers: Generating infinite random graphs

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The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…

Combinatorics · Mathematics 2024-02-08 Michela Ascolese , Matthias Lienau , Matthias Schulte , Anusch Taraz

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

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

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…

Probability · Mathematics 2011-04-20 Jonathan Jordan

Let $F$ be a probability distribution with support on the non-negative integers. Four methods for generating a simple undirected graph with (approximate) degree distribution $F$ are described and compared. Two methods are based on the so…

Probability · Mathematics 2015-09-30 Tom Britton , Maria Deijfen , Anders Martin-Löf

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…

Statistical Mechanics · Physics 2009-11-07 Jesper Dall , Michael Christensen

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…

Quantitative Methods · Quantitative Biology 2017-05-03 Frederic Y. Bois , Ghislaine Gayraud

Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G_1(m,n,t), the set of bipartite graphs with $m$ left vertices, n right vertices, t edges, and each vertex of degree at least one. We…

Probability · Mathematics 2007-05-23 Jonah Blasiak , Rick Durrett

Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…

Probability · Mathematics 2007-05-23 Bhupendra Gupta

Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\ random…

Probability · Mathematics 2015-09-24 Maria Deijfen , Ronald Meester

We investigate random processes for generating task-dependency graphs of order $n$ with $m$ edges and a specified number of initial vertices and terminal vertices. In order to do so, we consider two random processes for generating…

Discrete Mathematics · Computer Science 2023-05-10 Jesse Geneson , Shen-Fu Tsai

Given i.i.d. positive integer valued random variables D_1,...,D_n, one can ask whether there is a simple graph on n vertices so that the degrees of the vertices are D_1,...,D_n. We give sufficient conditions on the distribution of D_i for…

Probability · Mathematics 2007-05-23 Richard Arratia , Thomas M. Liggett

Given a dense countable set in a metric space, the infinite random geometric graph is the random graph with the given vertex set and where any two points at distance less than 1 are connected, independently, with some fixed probability. It…

Combinatorics · Mathematics 2021-05-21 Omer Angel , Yinon Spinka

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

Statistical Mechanics · Physics 2009-11-07 Duncan S. Callaway , John E. Hopcroft , Jon M. Kleinberg , M. E. J. Newman , Steven H. Strogatz

Bounded infinite graphs are defined on the basis of natural physical requirements. When specialized to trees this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two. We verify…

Condensed Matter · Physics 2009-11-07 Claudio Destri , Luca Donetti

This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…

Computer Vision and Pattern Recognition · Computer Science 2011-09-23 S. Deepak Srinivasan , Klaus Obermayer

Consider a random multigraph with given vertex degrees constructed by the configuration model. We give a new proof of the fact that, asymptotically for a sequence of such multigraphs with the number of edges tending to infinity, the…

Combinatorics · Mathematics 2013-07-25 Svante Janson

A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…

Combinatorics · Mathematics 2019-09-18 Yilun Shang

We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…

Statistical Mechanics · Physics 2009-11-07 Bo Soderberg

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Statistics Theory · Mathematics 2021-04-21 Anatol E. Wegner , Sofia Olhede