Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results …
C Greenhill - arXiv preprint arXiv:2201.04888, 2022 - arxiv.org
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a" …
P Gao, C Greenhill - Discrete Applied Mathematics, 2021 - Elsevier
The switch chain is a well-studied Markov chain which can be used to sample approximately uniformly from the set Ω (d) of all graphs with a given degree sequence d. Polynomial mixing …
G Amanatidis, P Kleer - Random Structures & Algorithms, 2020 - Wiley Online Library
The switch Markov chain has been extensively studied as the most natural Markov chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We show …
A Frieze, W Pegden - Proceedings of the 2023 Annual ACM-SIAM …, 2023 - SIAM
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to …
Consider the switch chain on the set of d-regular bipartite graphs on n vertices with 3≤ d≤ nc, for a small universal constant c> 0. We prove that the chain satisfies a Poincaré …
M Simper - Journal of Theoretical Probability, 2023 - Springer
The space of contingency tables with n total entries and fixed row and column sums is in bijection with parabolic double cosets of S n. Via this correspondence, the uniform …
D Allendorf, U Meyer, M Penschuck, H Tran - Journal of Parallel and …, 2023 - Elsevier
The uniform sampling of simple graphs matching a prescribed degree sequence is an important tool in network science, eg to construct graph generators or null-models. Here, the …
One of the simplest methods of generating a random graph with a given degree sequence is provided by the Monte Carlo Markov Chain method using switches. The switch Markov chain …