arXiv research

Study of special subgroups of automorphism groups of Kronrod-Reeb graphs for Morse functions on 2-torus.

Geometrically, the first Betti number of orbits is linked to the Kronrod-Reeb graph.

Let $M$ be a compact two-dimensional manifold and, $f \in C^{\infty}(M,\mathbb{R})$ be a Morse function, and $Γ_f$ be its Kronrod-Reeb graph. Denote by $\mathcal{O}_{f}=\{f \circ h \mid h \in \mathcal{D}\}$ the orbit of $f$ with respect to the natural right action of the group of diffeomorphisms $\mathcal{D}$ on $C^{\i…

Let $f:T^2\to\mathbb{R}$ be a Morse function on $2$-torus $T^2$ such that its Kronrod-Reeb graph $Γ(f)$ has exactly one cycle, i.e. it is homotopy equivalent to $S^1$. Under some additional conditions we describe a homotopy type of the orbit of $f$ with respect to the action of the group of diffeomorphism of $T^2$. Thi…

Let $f:T^2\to \mathbb{R}$ be Morse function on $2$-torus $T^2,$ and $\mathcal{O}(f)$ be the orbit of $f$ with respect to the right action of the group of diffeomorphisms $\mathcal{D}(T^2)$ on $C^{\infty}(T^2)$. Let also $\mathcal{O}_f(f,X)$ be a connected component of $\mathcal{O}(f,X)$ which contains $f.$ In the case …

Let $M$ be a connected orientable compact surface, $f:M\to\mathbb{R}$ be a Morse function, and $\mathcal{D}_{\mathrm{id}}(M)$ be the group of difeomorphisms of $M$ isotopic to the identity. Denote by $\mathcal{S}'(f)=\{f\circ h = f\mid h\in\mathcal{D}_{\mathrm{id}}(M)\}$ the subgroup of $\mathcal{D}_{\mathrm{id}}(M)$ c…

Let $f:M\to \mathbb{R}$ be a Morse function on a connected compact surface $M$, and $\mathcal{S}(f)$ and $\mathcal{O}(f)$ be respectively the stabilizer and the orbit of $f$ with respect to the right action of the group of diffeomorphisms $\mathcal{D}(M)$. In a series of papers the first author described the homotopy t…

Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.

Proposes MGMN for end-to-end graph similarity learning.

The paper explores graphons of line graphs from sparse finite graphs.

MxPool learns graph features from diverse graphs using a hierarchical structure.

Study the geometry of graph product extension graphs.

Graph neural network learns graph distances effectively.

Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.

Customized-GNN generates model-specific for each graph.

GRAPH-BERT uses only attention for graph representation learning.

Graph embedding leaks sensitive graph properties and subgraphs.

Characterizes graphs with leveled embeddings and introduces new graph invariants.

The paper shows conflict graphs of Petersen family graphs are mostly unbalanced.

Two new methods improve graph embedding without needing a complete graph structure.

We define a pseudo-inverse for line graphs using linear integer programming.

Develops method to create non-Abelian Ricci-flat graphs via bundles.

New method uses graph generative models for graph classification.

MathNet uses wavelets for graph representation and learning.

Unified framework for graph coarsening using node features and graph matrices.

A fast graph embedding method for large graphs.

Graph Laplacian spectrum serves as a robust feature representation.

Quadratic bounds found for graph dimensions.

Study classifies Halin graphs with positive curvature.

PSimGNN partitions graphs into subgraphs for efficient graph similarity computation.

We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform. Different from graph Fourier transform, graph wavelet transform can be obtained …

This paper develops graph theory for racks and quasigroups.

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and con…

We introduce a novel approach to graph-level representation learning, which is to embed an entire graph into a vector space where the embeddings of two graphs preserve their graph-graph proximity. Our approach, UGRAPHEMB, is a general framework that provides a novel means to performing graph-level embedding in a comple…

Graph Cascades rewire graphs to improve structure-aware learning.

CTGCN learns dynamic graph embeddings preserving both local and global graph structure.

Graphs can be fooled by small edge changes, but this work protects them.

The study bounds the effective diameter of graphs with positive Ollivier curvature.

Proposes DIAL-GNN for joint graph structure and embedding learning.

SpeqNets improve graph neural networks by scaling and adapting to graph sparsity.

Paper converts graph learning to lifelong learning.

Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the laten…

Proves Bochner's identity on graphs using a new auxiliary graph.

AgraSSt assesses graph generators using Stein operators and kernel discrepancies.

Proposes a graph pooling method leveraging node proximity for hierarchical graph representation learning.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampli…

Graph comparison ties to Alexandrov's theorems.

This study improves graph coarsening methods by preserving graph spectrum and distances.