Related papers: Recovering the Structure of Random Linear Graphs
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
Sentence ordering is to restore the original paragraph from a set of sentences. It involves capturing global dependencies among sentences regardless of their input order. In this paper, we propose a novel and flexible graph-based neural…
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
This paper studies how close random graphs are typically to their expectations. We interpret this question through the concentration of the adjacency and Laplacian matrices in the spectral norm. We study inhomogeneous Erd\"os-R\'enyi random…
Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the…
In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density…
How efficiently can we find an unknown graph using distance queries between its vertices? We assume that the unknown graph is connected, unweighted, and has bounded degree. The goal is to find every edge in the graph. This problem admits a…
We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a…
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
Node embedding learns low-dimensional vectors for nodes in the graph. Recent state-of-the-art embedding approaches take Personalized PageRank (PPR) as the proximity measure and factorize the PPR matrix or its adaptation to generate…
Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…
In graph analyses, directed edges are often approximated to undirected ones so that the adjacency matrices may be symmetric. However, such simplification has not been thoroughly verified. In this study, we investigate how directedness…
In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known…
Random walk-based node embedding algorithms have attracted a lot of attention due to their scalability and ease of implementation. Previous research has focused on different walk strategies, optimization objectives, and embedding learning…
We investigate rigidity-type problems on the real line and the circle in the non-generic setting. Specifically, we consider the problem of uniquely determining the positions of $n$ distinct points $V = {v_1, \ldots, v_n}$ given a set of…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
Uncover the vertices of a given graph, deterministic or random, in random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization…
Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…