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Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…
In this note, we analyze two random greedy processes on sparse random graphs and hypergraphs with a given degree sequence. First we analyze the matching process, which builds a set of disjoint edges one edge at a time; then we analyze the…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
Our previous paper applied a lopsided version of the Lov\'asz Local Lemma that allows negative dependency graphs to the space of random injections from an $m$-element set to an $n$-element set. Equivalently, the same story can be told about…
Recently, Davies, Jenssen, Perkins, and Roberts gave a very nice proof of the result (due, in various parts, to Kahn, Galvin-Tetali, and Zhao) that the independence polynomial of a $d$-regular graph is maximized by disjoint copies of…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
We find new upper bounds on the size of a minimum totally dominating set for random regular graphs and for regular graphs with large girth. These bounds are obtained through the analysis of a local algorithm using a method due to Hoppen and…
Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected.…
By implementing algorithmic versions of Sapozhenko's graph container methods, we give new algorithms for approximating the number of independent sets in bipartite graphs. Our first algorithm applies to $d$-regular, bipartite graphs…
We aim to learn a sparse and connected graph from sparse data, where the number of observations K can be substantially smaller than the signal dimension N for signals x in R^N, and the underlying distribution is unknown. In this severely…
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order $n$…
In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This enables us to enumerate loop-free digraphs and oriented graphs…
We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…
In this paper, we present two localized graph filtering based methods for interpolating graph signals defined on the vertices of arbitrary graphs from only a partial set of samples. The first method is an extension of previous work on…
It is known that under fixed-rate information constraints, adaptive quantizers can be used to stabilize an open-loop-unstable linear system on $\mathbb{R}^n$ driven by unbounded noise. These adaptive schemes can be designed so that they…
In the $d$-Scattered Set problem we are asked to select at least $k$ vertices of a given graph, so that the distance between any pair is at least $d$. We study the problem's (in-)approximability and offer improvements and extensions of…
We consider the problem of estimating the size of a maximum cut (Max-Cut problem) in a random Erd\H{o}s-R\'{e}nyi graph on $n$ nodes and $\lfloor cn \rfloor$ edges. It is shown in Coppersmith et al. ~\cite{Coppersmith2004} that the size of…
Vertex bisection is a graph partitioning problem in which the aim is to find a partition into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. We are interested in giving…
The asymptotic spectrum of graphs, introduced by Zuiddam (arXiv:1807.00169, 2018), is the space of graph parameters that are additive under disjoint union, multiplicative under the strong product, normalized and monotone under homomorphisms…