Related papers: The $\rho$-Capacity of a Graph

In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…

Can graph neural networks generalize to graphs that are different from the graphs they were trained on, e.g., in size? In this work, we study this question from a theoretical perspective. While recent work established such transferability…

We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…

As a result of the interaction of rapid development and competition in information technologies, the reliability of a network and how solid it remains is important. It is called the hat vulnerability of the network to measure the endurance…

The bloom of complex network study, in particular, with respect to scale-free ones, is considerably triggering the research of scale-free graph itself. Therefore, a great number of interesting results have been reported in the past,…

Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1 \leq r \leq n-2$, then there exists a configuration $p$ in general position in $R^r$ such that the bar framework $(G,p)$ is universally…

The edge-connectivity of a graph is the minimum number of edges whose deletion disconnects the graph. Let $\Delta(G)$ the maximum degree of a graph $G$ and let $\rho(G)$ be the spectral radius of $G$. In this article we present a lower…

Graph theory provides a primary tool for analyzing and designing computer communication networks. In the past few decades, Graph theory has been used to study various types of networks, including the Internet, wide Area Networks, Local Area…

Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study…

The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…

In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…

Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller compressed graphs capture relevant structural information for downstream tasks. There is a recent graph…

Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…

Let $G$ be a graph on $n$ vertices and $m$ edges. For $\alpha \in [0,1]$, the $A_{\alpha}$-matrix of $G$ is defined as $A_{\alpha}(G) = \alpha D(G) + (1- \alpha) A(G)$, where $A(G)$ is the adjacency matrix and $D(G)$ is the degree diagonal…

A Riemann-Roch theorem on graph was initiated by M. Baker and S. Norine. In their article [2], a Riemann-Roch theorem on a finite graph with uniform vertex-weight and uniform edge-weight was established and it was suggested a Riemann-Roch…

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph…

A graph $G$ is $\textit{universal}$ for a (finite) family $\mathcal{H}$ of graphs if every $H \in \mathcal{H}$ is a subgraph of $G$. For a given family $\mathcal{H}$, the goal is to determine the smallest number of edges an…

Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…

Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…