Related papers: A local graph rewiring algorithm for sampling span…
The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…
Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…
A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or intractable. A limited set of quantitative tools exist to assess the…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…
We introduce a new Markov Chain called the Cycle Walk for sampling measures of graph partitions where the partition elements have roughly equal size. Such Markov Chains are of current interest in the generation and evaluation of political…
Random walks on graphs are a fundamental concept in graph theory and play a crucial role in solving a wide range of theoretical and applied problems in discrete math, probability, theoretical computer science, network science, and machine…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is…
The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform…
We propose local-biased random walks on general networks where a Markovian walker can choose between different types of biases in each node to define transitions to its neighbors depending on their degrees. For this ergodic dynamics, we…
We are given an integer $d$, a graph $G=(V,E)$, and a uniformly random embedding $f : V \rightarrow \{0,1\}^d$ of the vertices. We are interested in the probability that $G$ can be "realized" by a scaled Euclidean norm on $\mathbb{R}^d$, in…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Random scale-free overlay topologies provide a number of properties like for example high resilience against failures of random nodes, small (average) diameter as well as good expansion and congestion characteristics that make them…
We study the problem of computing the diameter and the mean distance of a continuous graph, i.e., a connected graph where all points along the edges, instead of only the vertices, must be taken into account. It is known that for continuous…
We consider the problem of sampling a bipartite graph with given vertex degrees where a set $F$ of edges and non-edges which need to be contained is predefined. Our general result shows that the repeated swap of edges and non-edges in…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…