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In this paper we consider a simple Markov chain for bipartite graphs with given degree sequence on $n$ vertices. We show that the mixing time of this Markov chain is bounded above by a polynomial in $n$ in case of {\em semi-regular} degree…

Combinatorics · Mathematics 2021-01-01 Péter L. Erdös , Istán Miklós , Lajos Soukup

Markov chains are one of the well-known tools for modeling and analyzing stochastic systems. At the same time, they are used for constructing random walks that can achieve a given stationary distribution. This paper is concerned with…

Information Theory · Computer Science 2025-01-07 Saber Jafarizadeh

An edge switch is an operation which makes a local change in a graph while maintaining the degree of every vertex. We introduce a switch move, called a triangle switch, which creates or deletes at least one triangle. Specifically, a make…

Discrete Mathematics · Computer Science 2019-05-14 Colin Cooper , Martin Dyer , Catherine Greenhill

Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at…

Combinatorics · Mathematics 2021-07-28 Colin Cooper , Martin Dyer , Catherine Greenhill

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…

Methodology · Statistics 2015-03-19 Nanny Wermuth , Kayvan Sadeghi

We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\Delta$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if…

Data Structures and Algorithms · Computer Science 2017-08-10 Shai Vardi

We investigate the mixing rate of a Markov chain where a combination of long distance edges and non-reversibility is introduced: as a first step, we focus here on the following graphs: starting from the cycle graph, we select random nodes…

Probability · Mathematics 2018-02-13 Balázs Gerencsér , Julien Hendrickx

The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…

Probability · Mathematics 2025-08-13 Na Lin , Yuanyuan Liu , Aaron Smith

In network modeling of complex systems one is often required to sample random realizations of networks that obey a given set of constraints, usually in form of graph measures. A much studied class of problems targets uniform sampling of…

Combinatorics · Mathematics 2018-05-22 Péter L. Erdős , István Miklós , Zoltán Toroczkai

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

Quantitative Methods · Quantitative Biology 2011-12-21 E. S. Roberts , A. C. C. Coolen

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…

Quantum Physics · Physics 2022-09-14 Shantanav Chakraborty , Kyle Luh , Jérémie Roland

We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…

Physics and Society · Physics 2020-12-03 Szabolcs Horvát , Carl D. Modes

A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…

Probability · Mathematics 2020-06-19 Leran Cai , Thomas Sauerwald , Luca Zanetti

We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…

Discrete Mathematics · Computer Science 2007-05-23 Guy Melancon , Fabrice Philippe

Lifted Markov chains are Markov chains on graphs with added local "memory" and can be used to mix towards a target distribution faster than their memoryless counterparts. Upper and lower bounds on the achievable performance have been…

Optimization and Control · Mathematics 2017-05-24 Simon Apers , Francesco Ticozzi , Alain Sarlette

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…

Machine Learning · Computer Science 2023-12-18 Eddie Seabrook , Laurenz Wiskott

Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution.…

Numerical Analysis · Mathematics 2022-09-07 Konstantin Avrachenkov , Patrick Brown , Nelly Litvak

Ge and Stefankovic have recently introduced a novel two-variable graph polynomial. When specialised to a bipartite graphs G and evaluated at the point (1/2,1) this polynomial gives the number of independent sets in the graph. Inspired by…

Probability · Mathematics 2012-01-18 Leslie Ann Goldberg , Mark Jerrum

We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…

Methodology · Statistics 2025-05-20 Daphne Aurouet , Valentin Patilea

The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…

Social and Information Networks · Computer Science 2023-05-31 Upasana Dutta , Bailey K. Fosdick , Aaron Clauset