arXiv research

Paper proves edge-connectivity equals minimum degree for graphs with non-negative curvature.

Every infinitely edge-connected graph has a minor of Farey graph or $T_{\aleph_0}\ast t$.

In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general…

When $S$ is a closed, orientable surface with genus $g(S) \geq 2$, we show that the automorphism group of the compression body graph $\mathcal{CB}(S)$ is the mapping class group. Here, vertices are compression bodies with exterior boundary $S$, and edges connect pairs of compression bodies where one contains the other.

Most real-world networks exhibit community structure, a phenomenon characterized by existence of node clusters whose intra-edge connectivity is stronger than edge connectivities between nodes belonging to different clusters. In addition to facilitating a better understanding of network behavior, community detection fin…

We extend the edge version of the classical Menger's Theorem for undirected graphs to $n$-dimensional simplicial complexes with chains over the field $\mathbb{F}_2$. The classical Menger's Theorem states that two different vertices in an undirected graph can be connected by $k$ pairwise edge-disjoint paths if, and only…

Automorphisms of fine curve graphs match surface homeomorphisms for planar surfaces.

Automorphisms of fine 1-curve graph linked to surface homeomorphisms.

We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating examples, we have corrected previous misunderstandings on the topological prope…

Connected graph for twice-punctured torus curves.

We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…

From computational geometry comes the notion of a Gabriel graph of a point set in the plane. The Gabriel graph consists of those edges connecting two points of the point set such that the circle whose diameter is the edge does not contain any point of the point set in its interior. We define a generalization of the Gab…

This paper presents a methodology for image classification using Graph Neural Network (GNN) models. We transform the input images into region adjacency graphs (RAGs), in which regions are superpixels and edges connect neighboring superpixels. Our experiments suggest that Graph Attention Networks (GATs), which combine g…

Graph Convolutional Networks (GCNs) have shown very powerful for graph data representation and learning tasks. Existing GCNs usually conduct feature aggregation on a fixed neighborhood graph in which each node computes its representation by aggregating the feature representations of all its neighbors which is biased by…

The fine curve graph is hyperbolic and contains all countable graphs as induced subgraphs.

Machine learning models that take computer program source code as input typically use Natural Language Processing (NLP) techniques. However, a major challenge is that code is written using an open, rapidly changing vocabulary due to, e.g., the coinage of new variable and method names. Reasoning over such a vocabulary i…

New findings on hyperbolicity of fine curve graphs and their subgraphs.

New framework for dense weighted networks with community-specific patterns.

Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploi…

New algorithm assesses credit risk in multilayer networks over time.

Graph neural networks improve El Niño forecasts.

Clustering is fundamental for gaining insights from complex networks, and spectral clustering (SC) is a popular approach. Conventional SC focuses on second-order structures (e.g., edges connecting two nodes) without direct consideration of higher-order structures (e.g., triangles and cliques). This has motivated SC ext…

Development of stock networks is an important approach to explore the relationship between different stocks in the era of big-data. Although a number of methods have been designed to construct the stock correlation networks, it is still a challenge to balance the selection of prominent correlations and connectivity of …

The paper investigates how Global Self-attention improves GCNs.

Graph neural networks (GNNs) have received much attention recently because of their excellent performance on graph-based tasks. However, existing research on GNNs focuses on designing more effective models without considering much about the quality of the input data. In this paper, we propose self-enhanced GNN (SEG), w…

The study determines $\mathbb{Z}_2$-Thurston norms in Sol manifolds and embeds non-orientable surfaces.

New IPL graphs identified and conditions for their projective embeddings established.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional…

New method clusters directed and undirected graphs without losing directional information.

Optimal graph classification uses message-passing neural networks.

In this paper, we consider the problem of estimating the underlying graph associated with an Ising model given a number of independent and identically distributed samples. We adopt an \emph{approximate recovery} criterion that allows for a number of missed edges or incorrectly-included edges, in contrast with the widel…

Graph-Triggered Bandits unify rested and restless bandits with graph-defined arm interactions.

Method quantifies uncertainties in complex MRF models.

Automatic estimation of relative difficulty of a pair of questions is an important and challenging problem in community question answering (CQA) services. There are limited studies which addressed this problem. Past studies mostly leveraged expertise of users answering the questions and barely considered other properti…

GNNGuard defends Graph Neural Networks against structural perturbations.

New findings on strong convexity in triangulations of convex polygons.

Discrete knot theory models use lattice-filtered graphs to detect merging knot components.

Crop yield forecasting is the methodology of predicting crop yields prior to harvest. The availability of accurate yield prediction frameworks have enormous implications from multiple standpoints, including impact on the crop commodity futures markets, formulation of agricultural policy, as well as crop insurance ratin…

Quantum GNNs outperform classical GNNs in jet tagging.

The paper defines and studies discrete p-density and compression-radius profiles of lattice knots.

Estimates network structure from correlated node outputs of wide-sense stationary processes.

Can we identify node labels from graph labels?