Related papers: Connes embeddability of graph products
We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well as rough isometries.
Graph embedding, especially as a subgraph of a grid, is an old topic in VLSI design and graph drawing. In this paper, we investigate related questions concerning the complexity of embedding a graph $G$ in a host graph that is the strong…
A connected graph $G$ is of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently if the distance matrix is conditionally negative definite, or equivalently if the quadratic embedding constant $\mathrm{QEC}(G)$ is…
We show that the stable cohomology of the algebraic polyvector fields on $\mathbb{R}^n$, with values in the adjoint representation is the symmetric product space on the cohomology of M. Kontsevich's graph complex, up to some known classes.
We consider for two based graphs $G$ and $H$ the sequence of graphs $G_k$ given by the wedge sum of $G$ and $k$ copies of $H$. These graphs have an action of the symmetric group $\Sigma_k$ by permuting the $H$-summands. We show that the…
A "folklore conjecture, probably due to Tutte" (as described in [P.D. Seymour, Sums of circuits, Graph theory and related topics (Proc. Conf., Univ. Waterloo, 1977), pp. 341-355, Academic Press, 1979]) asserts that every bridgeless cubic…
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…
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…
It is well-known that a minimal graph of codimension one is stable, i.e. the second variation of the area functional is non-negative. This is no longer true for higher codimensional minimal graphs. In this note, we prove that a minimal…
We present a new sufficient condition on stability number and toughness of the graph to have an f-factor.
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
The graph-based model can help to detect suspicious fraud online. Owing to the development of Graph Neural Networks~(GNNs), prior research work has proposed many GNN-based fraud detection frameworks based on either homogeneous graphs or…
Given a function $g=g(n)$ we let ${\mathcal E}^g$ be the class of all graphs $G$ such that if $G$ has order $n$ (that is, has $n$ vertices) then it is embeddable in some surface of Euler genus at most $g(n)$, and let ${\widetilde{\mathcal…
Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…
In this note, we study the equivalence of Morse and stable subgroups in the framework of the coset intersection complex. Under certain conditions on a coset intersection complex of a group, we prove that infinite-index Morse subgroups are…
We are presenting a simple and numerical stable algorithm for the solution of the cone projection problem which is suitable for relative small data sets and for simulation purposes needed for convexity tests. Not even one pseudo-inverse…
Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…