arXiv research

Gaussian processes classify graphs using vertex and edge features.

Graph cross network improves graph classification accuracy.

Paper studies vertex correspondence recovery in correlated graphs with node features.

In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex grid structures, and define a new vertex convolution operation by adopting a set of…

Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list. Previous work has yielded several approaches to this problem, with theoretical re…

Graph matching with feature vectors is solved using a two-layer graph neural network.

Pyramidal GNN combines RC and pooling for efficient graph embeddings.

The paper explores how to find relevant vertices in one graph using another graph's attributes and structure.

DeepMap learns deep graph representations via CNNs, improving graph classification performance.

A graph neural network transforms features in each vertex's neighborhood into a vector representation of the vertex. Afterward, each vertex's representation is used independently for predicting its label. This standard pipeline implicitly assumes that vertex labels are conditionally independent given their neighborhood…

Proposes a new method to describe graph vertex features using characteristic functions.

This paper examines how graph topology affects adversarial attacks on vertex classification.

Vertex distortion detects if a knot is unknot.

Given a time series of graphs G(t) = (V, E(t)), t = 1, 2, ..., where the fixed vertex set V represents "actors" and an edge between vertex u and vertex v at time t (uv \in E(t)) represents the existence of a communications event between actors u and v during the tth time period, we wish to detect anomalies and/or chang…

New algorithms SVCA and SSPA improve robustness to noise in nonnegative matrix factorization.

The study finds the bounds of vertex orbits in maps derived from specific lattices.

A piecewise flat Finsler metric on a triangulated surface $M$ is a metric whose restriction to any triangle is a flat triangle in some Minkowski space with straight edges. One of the main purposes of this work is to study the properties of geodesics on a piecewise flat Finsler surface, especially when it meets a vertex…

Given a vertex of interest in a network $G_1$, the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network $G_2$. A vertex nomination scheme produces a list of the vertices in $G_2$, ranked according to how likely they are judged to be the corresponding vertex of …

634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations of octonionic projective plane.

A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear sequences of nodes to create embeddings using a neural network. In this paper, we pr…

Researchers clarify modular group representations and vertex operator algebras for 3d invariants.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through an embedding method provides superior performance in many real-world applicatio…

Defines formal vertex laws related to Lie conformal algebras.

Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types $[p^3, 3]$ for $p \equiv 1$ (mod $6$), but there doesn't exist vertex-transitive map of such types. In particu…

The study examines vertices in curves with singular points in the Euclidean plane.

Vertex distortion measures how far lattice knots deviate from straight lines.

Graph neural networks suffer from oversmoothing, but adding residual connections helps.

For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, w…

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function $κ$, provided that the latent positions are i.i.d. from some distribution F. We then consider the exploitation task of vertex classi…

We prove that there exists a geodesic trajectory on the dodecahedron from a vertex to itself that does not pass through any other vertex.

Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We present a minimal crystallization of the standard PL K3 surface. In combination w…

New proof for global rigidity of vertex scaling on polyhedral surfaces.

This is the third of a series of papers on a new equivariant cohomology that takes values in a vertex algebra, and contains and generalizes the classical equivariant cohomology of a manifold with a Lie group action a la H. Cartan. In this paper, we compute this cohomology for spheres and show that for any simple connec…

Proves a generalized Whitehead cut vertex lemma for tree groups.

Solves Skopenkov's problem on graph embedding criteria.

A semi-regular tiling of the hyperbolic plane is a tessellation by regular geodesic polygons with the property that each vertex has the same vertex-type, which is a cyclic tuple of integers that determine the number of sides of the polygons surrounding the vertex. We determine combinatorial criteria for the existence, …

Efficient method for vertex embedding and community detection.

New invariants distinguish spatial graphs not previously possible.

The paper concerns discrete versions of the three well-known results of projective differential geometry: the four vertex theorem, the six affine vertex theorem and the Ghys theorem on four zeroes of the Schwarzian derivative. We study geometry of closed polygonal lines in $\bbRP^d$ and prove that polygons satisfying a…

Proofs for Moon's theorem and its generalization.

Investigates the vertex curve of smooth surfaces in 3D space, connecting geometry and image analysis.

Let $M$ be a Riemannian manifold. For $p\in M$, the tensor algebra of the negative part of the (complex) affinization of the tangent space of $M$ at $p$ has a natural structure of a meromorphic open-string vertex algebra. These meromorphic open-string vertex algebras form a vector bundle over $M$ with a connection. We …

Study finds root vertex in large networks with high probability.

A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.

Marked vertex diagrams provide a combinatorial way to represent knotted surfaces in $\mathbb{R}^4$; including virtual crossings allows for a theory of virtual knotted surfaces and virtual cobordisms. Biquandle counting invariants are defined only for marked vertex diagrams representing knotted orientable surfaces; we e…

Consider a group G and a family $\mathcal{A}$ of subgroups of G. We say that vertex finiteness holds for splittings of G over $\mathcal{A}$ if, up to isomorphism, there are only finitely many possibilities for vertex stabilizers of minimal G-trees with edge stabilizers in $\mathcal{A}$. We show vertex finiteness when G…

Researchers link vertex algebras to non-Kähler solutions of the Hull-Strominger system.