Related papers: Graph Multivector Persistence: A Unified Framework…
We present a method which provides a unified framework for most stability theorems that have been proved in graph and hypergraph theory. Our main result reduces stability for a large class of hypergraph problems to the simpler question of…
We consider a Chinese remainder theorem for (labeled) graphs. For $X$ a GKM $T$-variety and $Y$ an invariant subvariety, we use this to give a condition for surjectivity of the restriction map $H^*(X) \to H^*(Y)$. In particular, this…
We address the problem of estimating multiple modes of a multivariate density using persistent homology, a central tool in Topological Data Analysis. We introduce a method based on the preliminary estimation of the $H_0$-persistence diagram…
A graph with convex quadratic stability number is a graph for which the stability number is determined by solving a convex quadratic program. Since the very beginning, where a convex quadratic programming upper bound on the stability number…
The graph reconstruction conjecture asserts that every simple graph on at least three vertices is uniquely determined by its deck of vertex-deleted subgraphs. In this expository article we survey the conjecture and present an…
Generating graph structures is a challenging problem due to the diverse representations and complex dependencies among nodes. In this paper, we introduce Graph Variational Recurrent Neural Network (GraphVRNN), a probabilistic autoregressive…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of Persistent Homology in this context, its interaction with the ordering and the repercussions of the process…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
When persistence diagrams are formalized as the Mobius inversion of the birth-death function, they naturally generalize to the multi-parameter setting and enjoy many of the key properties, such as stability, that we expect in applications.…
Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node…
This paper studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron-Frobenius theorem for nonnegative tensors with respect to the tensors Z-eigenvalues and Z-eigenvectors. Firstly, for a…
Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for…
We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy…
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycles, complete graphs, wheel graphs, hypercubes, complete…
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…
We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this…
Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…