Related papers: Shift-Coupling of Random Rooted Graphs and Network…
Let red and blue points be distributed on $\mathbb{R}$ according to two independent Poisson processes $\mathcal{R}$ and $\mathcal{B}$ and let each red (blue) point independently be equipped with a random number of half-edges according to a…
We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…
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…
This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…
Network moments--rescaled counts of motifs such as stars and triangles--are fundamental summaries of network structure, widely used in goodness-of-fit testing, model selection, and network comparison. While the univariate distribution of a…
We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
Given a finite sequence of graphs, e.g., coming from technological, biological, and social networks, the paper proposes a methodology to identify possible changes in stationarity in the stochastic process generating the graphs. In order to…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
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 the classical Erd\"os-R\'enyi random graph G(n,p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n,p) is homogeneous in the sense that all vertices have the same…
We study the properties of conformal prediction for network data under various sampling mechanisms that commonly arise in practice but often result in a non-representative sample of nodes. We interpret these sampling mechanisms as selection…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\ random…
Transporter Net is a recently proposed framework for pick and place that is able to learn good manipulation policies from a very few expert demonstrations. A key reason why Transporter Net is so sample efficient is that the model…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
In majority dynamics, agents located at the vertices of an undirected simple graph update their binary opinions synchronously by adopting those of the majority of their neighbors. On infinite unimodular transitive graphs (e.g., Cayley…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers $\mathbb{N}$ via a Poisson point process with mean measure $\Lambda$ on the power set of $\mathbb{N}$. Each $E\in\cate$…