Related papers: Information Limits for Detecting a Subhypergraph
This article presents a theoretical investigation of generalized encoded forms of networks in a uniform multidimensional space. First, we study encoded networks with (finite) arbitrary node dimensions (or aspects), such as time instants or…
In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the…
This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the…
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…
In statistical network analysis, models for binary adjacency matrices satisfying vertex exchangeability are commonly used. However, such models may fail to capture key features of the data-generating process when interactions, rather than…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
The use of tools from analysis to approach problems in graph theory has become an active area of research. Usually such methods are applied to problems involving dense graphs and hypergraphs; here we give the an extension of such methods to…
Ryser's Conjecture states that any $r$-partite $r$-uniform hypergraph has a vertex cover of size at most $r - 1$ times the size of the largest matching. For $r = 2$, the conjecture is simply K\"onig's Theorem and every bipartite graph is a…
In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the $m-$uniform sub-hypergraph stochastic block model ($m-$ShSBM). Under the…
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting…
A celebrated theorem of Pippenger states that any almost regular hypergraph with small codegrees has an almost perfect matching. We show that one can find such an almost perfect matching which is `pseudorandom', meaning that, for instance,…
We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly…
In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A…
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs.…
A Berge copy of a graph is a hypergraph obtained by enlarging the edges arbitrarily. Gr\'osz, Methuku and Tompkins in 2020 showed that for any graph $F$, there is an integer $r_0=r_0(F)$, such that for any $r\ge r_0$, any $r$-uniform…
We analyze the necessary number of samples for sparse vector recovery in a noisy linear prediction setup. This model includes problems such as linear regression and classification. We focus on structured graph models. In particular, we…
In this paper, we study the sample complexity lower bounds for the exact recovery of parameters and for a positive excess risk of a feed-forward, fully-connected neural network for binary classification, using information-theoretic tools.…
The group synchronization problem is to estimate unknown group elements at the vertices of a graph when given a set of possibly noisy observations of group differences at the edges. We consider the group synchronization problem on finite…
Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the…