Related papers: Mixing Time of Vertex-Weighted Exponential Random …
We study the problem of efficiently approximating the \textit{effective resistance} (ER) on undirected graphs, where ER is a widely used node proximity measure with applications in graph spectral sparsification, multi-class graph…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Statistical analysis of social networks provides valuable insights into complex network interactions across various scientific disciplines. However, accurate modeling of networks remains challenging due to the heavy computational burden and…
Classical spectral graph theory characterizes graphs with logarithmic mixing time. In this work, we present a combinatorial characterization of graphs with constant mixing time. The combinatorial characterization is based on the small-set…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…
In this article, we derive a sharp mixing time estimate of the Glauber dynamics for the Curie-Weiss-Potts model in the low-temperature regime. In contrast to the high-temperature regime studied by Cuff et al. (J. Stat. Phys. 149: 432-477,…
In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
We prove a cutoff for the random walk on random $n$-lifts of finite weighted graphs, even when the random walk on the base graph $\mathcal{G}$ of the lift is not reversible. The mixing time is w.h.p. $t_{mix}=h^{-1}\log n$, where $h$ is a…
Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the…
We characterize the uniqueness condition in the hardcore model for bipartite graphs with degree bounds only on one side, and provide a nearly linear time sampling algorithm that works up to the uniqueness threshold. We show that the…
The antiferromagnetic Ising model samples subsets of vertices of a graph with weight decaying exponentially in the number of edges induced. We study the problem of sampling from this model on the class of bipartite, regular graphs with good…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
Random walk-based sampling methods are gaining popularity and importance in characterizing large networks. While powerful, they suffer from the slow mixing problem when the graph is loosely connected, which results in poor estimation…
We investigate the computational complexity of the exponential random graph model (ERGM) commonly used in social network analysis. This model represents a probability distribution on graphs by setting the log-likelihood of generating a…
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…
In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics. The Glauber dynamics is a Markov chain that sequentially updates individual nodes (variables) in a…
The Waxman random graph is a generalisation of the simple Erd\H{o}s-R\'enyi or Gilbert random graph. It is useful for modelling physical networks where the increased cost of longer links means they are less likely to be built, and thus less…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…