There is a well-known connection between hypergraphs and bipartite graphs, obtained by
treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite …

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" …

We consider the spectral gap of a uniformly chosen random (d 1, d 2)-biregular bipartite
graph G with| V 1|= n,| V 2|= m, where d 1, d 2 could possibly grow with n and m. Let A be the …

For reversible Markov chains on finite state spaces, we show that the modified log-Sobolev
inequality (MLSI) can be upgraded to a log-Sobolev inequality (LSI) at the surprisingly low …

Consensus-based data aggregation in d-regular bipartite graphs poses a challenging task
for the scientific community since some of these algorithms diverge in this critical graph …

In this work we develop a comparison procedure for the modified log-Sobolev inequality
(MLSI) constants of two reversible Markov chains on a finite state space. Efficient …

We discuss sequential stub matching for directed graphs and show that this process can be
used to sample simple digraphs with asymptotically equal probability. The process starts …

The triangle switch Markov chain is designed to generate random graphs with given degree
sequence, but having more triangles than would appear under the uniform distribution …

We establish cutoff for a natural random walk (RW) on the set of perfect matchings (PM s),
based on “rewiring”. An n-PM is a pairing of 2 n objects. The k-PM RW selects k pairs …

Mahlmann and Schindelhaue (2005) proposed the following simple process, called flip-
chain, for transforming any given connected d-regular graph into ad-regular expander: In …