arXiv research

Study of graphs interpolating curve and pants graphs, providing formulae and geometry classifications.

Study the geometry of graph product extension graphs.

Graph dynamics link combinatorics to geometry, revealing manifold intersections and stability.

Finslerian graph neural networks recover nonlinear diffusion geometry

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $ΔG$ of the graph and try to improve generalization. Based on quantum information geometry, $ΔG$ can be characterized by the eigendecomposition of the graph Laplaci…

Liouville theorems extended to graphs with bounded geometry.

Study on planar graphs in Poincare model of hyperbolic geometry.

Study of mapping class groups on infinite graphs, focusing on their large-scale geometry.

Spectral graph sparsification preserves geometry of GNN embeddings.

Sheaves on graphs link to noncommutative geometry.

Enhances knowledge graph completion with mixed geometry tensor factorization.

Study of graphs from hexagon decompositions of surfaces.

Study connects flow dynamics to 3D geometry via surface intersections.

Study shows saddle connection graph's geometry and quasi-isometry properties.

Graph Ricci flow reveals hidden hierarchies in stock market correlations.

We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph respectively. The central result in this paper is the fact that each right-angled Artin group acts acylindrically on its extension graph. From this result we …

Researchers reconstruct algebraic maps onto curves based on prescribed Reeb graphs.

Study $G_2$-manifolds from symplectic $SU(3)$-manifolds with $T^2$-symmetry.

A new algorithm improves sampling for graph learning models.

Neural networks' feature geometry evolves like discrete Ricci flow.

The study combines graph-minors and metric spaces, answering some questions and conjectures.

We investigate the geometry of the graphs of nonseparating curves for surfaces of finite positive genus with potentially infinitely many punctures. This graph has infinite diameter and is known to be Gromov hyperbolic by work of the author. We study finite covers between such surfaces and show that lifts of nonseparati…

We prove that the Cayley graph and the coset geometry of the von Dyck group $D(a,b,c)$ are linked by a vertex-to-edge duality.

Study large-scale geometry of graph braid groups via cubical structures.

The paper bounds higher Steklov eigenvalues of graphs on surfaces.

Develops methods to analyze manifold singularities using graph Laplacian.

Surveying connections between graph combinatorics and algebraic right-angled Artin groups.

This is a survey paper. We study the Ricci curvature and spectrum of graphs, as well as the exterior forms and deRahm cohomology on graphs.

New method separates graph structure from node attributes to recover lost signal.

Graph kernels for metric graphs using tropical algebra.

The study compares lamplighter graphs up to quasi-isometry using coarse topology.

The paper solves graph realization problems for Reeb graphs of Morse functions.

We show that there are minimal graphs in R^{n+1} whose intersection with the portion of the horizontal hyperplane contained in the unit ball has any prescribed geometry, up to a small deformation. The proof hinges on the construction of minimal graphs that are almost flat but have small oscillations whose geometry we c…

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the construction is sufficiently regular and uniform, then the notions of metric, geodesic and…

We explore the use of graph networks to deal with irregular-geometry detectors in the context of particle reconstruction. Thanks to their representation-learning capabilities, graph networks can exploit the full detector granularity, while natively managing the event sparsity and arbitrarily complex detector geometries…

Metric graphs have subgraphs with entropy at least λ.

Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on this theory, we demonstrate the efficiency of Subspace Clustering in fairly broad…

GS-B$^3$SE improves label shift estimation by smoothing priors on a graph.

This paper connects graph curvature to community structure.

The paper explores representations of graph manifolds to Seifert motion groups.

Enhances graph modeling with hyperbolic geometry and variational inference.

We address the problem of setting the kernel bandwidth used by Manifold Learning algorithms to construct the graph Laplacian. Exploiting the connection between manifold geometry, represented by the Riemannian metric, and the Laplace-Beltrami operator, we set the bandwidth by optimizing the Laplacian's ability to preser…

Neural network learns from higher-order connections in molecules.

The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity assumption. In a recent paper, Brendle and Wang find a sufficient condition for …

Study reveals limits of detecting local geometry in random graphs.

A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their a…

New research shows hyperbolic embeddings are useful for global consistency tasks in graphs.

Interpolates mean shift and spectral clustering on graphs.