New method assesses graph generators using graph classifiers.
problem Quantifying how well generative models create realistic graphs.
method Using graph classifiers to evaluate synthesized graphs against real ones.
result Inability of a classifier to distinguish real from synthetic graphs indicates poor model performance.
Study classifies Halin graphs with positive curvature.
problem Classifying Halin graphs with specific curvature.
method Analyzing generalized Halin graphs formed by connecting tree leaves.
result Identified all generalized Halin graphs with positive Lin-Lu-Yau curvature.
The study classifies graphs with specific curvature and maximum degree.
problem Graphs with nonnegative Ricci curvature and maximum degree constraints.
method Classification of graphs with Lin-Lu-Yau-Ollivier Ricci curvature, maximum degree ≤ 3, and diameter ≥ 6.
result Classification of graphs meeting the specified criteria.
We classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices. For graphs in these families, we verify a conjecture presented in Adams' "The Knot Book": If a vertex is remo…
Classifies graph configuration spaces homeomorphic to manifolds.
problem Classifying graph configuration spaces homeomorphic to manifolds.
method Developed techniques to translate topological properties into graph theoretic ones.
result Extended Abrams' work to classify certain graph configuration spaces.
Classifies colored links and spatial graphs up to colored link-homotopy.
problem Classifying colored links and spatial graphs up to colored link-homotopy.
method Using Habegger-Lin theory for colored string links, and extending to colored links and spatial graphs.
result Classification of colored links and spatial graphs up to colored link-homotopy.
Classifies solitons for surface diffusion flow of graphs.
problem Classifying solitons for surface diffusion flow of graphs.
method Classifies solitons including equilibria, self-similar solutions, and travelling waves.
result Classified solitons for surface diffusion flow of entire graphs.
We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respe…
The study classifies graphs on surfaces with positive curvature properties.
problem Classifying graphs on surfaces with specific curvature properties.
method Using medial graphs and classification techniques.
result Complete classification of graphs on surfaces with positive Forman curvature and corner curvature.
Flexible per-class regularization improves binary classifiers.
problem Improving binary classifiers by addressing outliers and class imbalance.
method Graph-based adaptive regularization with flexible per-class thresholds.
result Flexible thresholds improve classifier performance and address class imbalance.
Method generates counterfactual explanations for graph classifiers.
problem Generating high-quality explanations for graph predictions.
method Permutation equivariant graph variational autoencoder to traverse latent space.
result Empirically validated model is high-performing and robust.
Develops structured noise for more accurate graph classifier robustness certificates.
problem Isotropic noise limits robustness certificates for graph classifiers.
method Randomized smoothing with anisotropic noise distribution.
result Structured-aware robustness certificates provide more accurate predictions.
The paper classifies virtual knot polynomials and trivalent graph invariants using skein theory.
problem Classifying virtual knot polynomials and trivalent graph invariants with specific conditions.
method Skein-theoretic techniques applied to classify invariants with smallness conditions.
result Classification of all non-trivial invariants of trivalent graphs and skein theories of virtual tangles.
PolyGraph Discrepancy improves graph generative model evaluation.
problem Inability of existing metrics to provide an absolute performance measure and comparability across different graph descriptors.
method Approximates Jensen-Shannon distance using binary classifiers trained to distinguish between real and generated graphs.
result PGD provides a more robust and insightful evaluation compared to MMD metrics.
The paper classifies palettes of Dehn colorings for spatial graphs.
problem Classifying spatial graph diagrams using Dehn colorings.
method Examining vertex conditions and palettes for spatial graphs.
result Spatial graphs can be distinguished by the number of Dehn colorings with specific palettes.
Graph-based multi-label classifier extends CULP for multi-label data.
problem Solving multi-label classification problems.
method Extends CULP algorithm to handle multi-label data.
result Competitive results compared to cutting-edge multi-label classifiers.
Indirect attacks can fool graph classifiers even with poisoned neighbors.
problem How to evaluate and defend graph convolutional neural networks against indirect adversarial attacks.
method Proposed a method to generate adversarial perturbations on a single node far from the target.
result 99% attack success rate within two-hops from the target in two datasets.
Graph-Hist classifies social media graphs using feature histograms.
problem Classifying large, sparse social media graphs.
method Extracts latent features, bins nodes, and classifies based on multi-channel histograms.
result Improves bot detection in social media graphs.
We classify which complete multipartite graphs are intrinsically chiral.
A novel multi-layer architecture for one-class classification using graph-embedded kernel ridge regression.
problem Outlier detection in one-class classification using only normal samples.
method Stacking various Graph-Embedded Kernel Ridge Regression (KRR) based Auto-Encoders in a hierarchical fashion.
result The proposed method outperforms existing one-class classifiers on 21 benchmark datasets.
New method certifies deep graph classifiers with tighter risk bounds.
problem Certifying the reliability of deep graph classifiers.
method Linearized deep assignment flows with random initial conditions, using PAC-Bayes risk certification.
result Computes tighter out-of-sample risk certificates efficiently.
This paper classifies chiral graphs up to size 12.
problem Understanding the chirality of simple graphs to predict molecular behavior.
method Classifying minor minimal intrinsically chiral graphs among simple graphs of size up to 12.
result Complete set of minor minimal graphs for intrinsic properties of chiral molecules.
Paper proposes a robust deep graph-based classifier for noisy labels.
problem Difficulty in feature learning with noisy training labels.
method Convolutional neural networks with graph Laplacian regularization (GLR).
result Proposed method outperforms state-of-the-art classifiers on noisy datasets.
Study classifies graphs in Euclidean and non-Euclidean spaces with specific curvature conditions.
problem Classifying graphs with prescribed curvature in various spaces.
method Proves rigidity and classification results for graphs in Riemannian manifolds, focusing on R2 and R3. result Provides general splitting theorems for graphs in these settings.
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures, are nowadays available and tested for various datasets of labeled graphs. However…
The study connects spheres in specific surface curve graphs, proving connectivity and classifying components.
problem Proving connectivity and classifying components of spheres in curve graphs of low and medium complexity surfaces.
method Analyzing specific surfaces Σ2,0,Σ1,3,Σ0,6 and Σ0,5,Σ1,2, proving connectivity and classifying components. result Spheres of any radius are connected in Σ2,0,Σ1,3,Σ0,6, and the union of two consecutive spheres is connected in Σ0,5 and Σ1,2. Study classifies graphs with positive curvature without quadrilaterals.
problem Classifying graphs with positive Lin-Lu-Yau curvature without quadrilaterals.
method Definition of Ricci curvature on graphs, limit-free formulation using graph Laplacian.
result Identifies all simple connected C4-free graphs with positive Lin-Lu-Yau curvature.
Optimal graph classification uses message-passing neural networks.
problem Node classification on sparse graphs with fixed feature dimensions.
method Asymptotic local Bayes optimality, message-passing graph neural networks.
result Optimal message-passing architecture interpolates between MLP and convolution.
A hex sphere is a singular Euclidean sphere with four cones points whose cone angles are (integer) multiples of 2*pi/3 but less than 2*pi. Given a hex sphere M, we consider its Voronoi decomposition centered at the two cone points with greatest cone angles. In this paper we use elementary Euclidean geometry to describe…
The paper classifies when certain graph braid groups are 3-manifold groups.
problem Identifying when graph braid groups are 3-manifold groups.
method Analyzing the graph braid groups B3(Θm) for specific graphs Θm. result The paper shows that B3(Θ5) is a 3-manifold group, but B3(Θm) is not quasi-isometric to a 3-manifold group for m≥7. Classifies fibering of state surfaces for various knot families.
problem Determining which state surfaces are fibered.
method Algebraic characterization of fibers from state graphs, decomposing graphs into planar components.
result Characterizes fibering for many families of state surfaces.
Unified approach to multiclass classification using Gabriel graphs.
problem Improving multiclass classification accuracy and efficiency.
method Integrates Gabriel graphs for binary and multiclass classification, proposing new activation functions and support edge neurons.
result Experimental results show superior performance compared to previous GG-based classifiers.
Study groups that can embed Heawood graph in 3D space.
problem Classifying topological symmetry groups of the Heawood graph.
method Analyzing embeddings of the Heawood graph in S3. result Identified all possible groups as topological symmetry groups.
Classifies SU(2)-abelian graph manifolds with a single JSJ torus.
problem Classifying SU(2)-abelian 3-manifolds.
method Using Seifert coefficients and Heegaard Floer homology.
result SU(2)-abelian graph manifolds are Heegaard Floer homology L-spaces.
Gaussian processes classify graphs using vertex and edge features.
problem Graph classification in machine learning.
method Transform graph features into spectral Euclidean features, apply Hodge decomposition.
result Gaussian processes can classify graphs using vertex and edge features.
Study of pure mapping class groups on infinite graphs.
problem Classifying graphs with specific mapping class groups.
method Completely classified graphs with pure mapping class groups.
result Established semidirect product decomposition and computed first integral cohomology.
A novel algorithm CULP uses link prediction for graph classification.
problem Graph classification using unlabeled data.
method CULP uses a Label Embedded Graph (LEG) and a link predictor to classify unlabeled nodes.
result CULP and CULM show high accuracy and competitiveness with existing graph classifiers.
LAGCN improves GCN performance by identifying and using valuable neighbors.
problem Existing GCN models do not identify valuable neighbors, potentially harming performance.
method LAGCN introduces a label-aware edge classifier to refine the graph and enhance learning performance.
result LAGCN significantly improves node classification performance on benchmark datasets.
Paper uses graph structure to improve Wikipedia classification.
problem Classifying Wikipedia into a fine-grained named entity hierarchy.
method Explores graph descriptors and weighted models for feature vectors.
result Graph information reduces sparsity and improves classification.
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…
Proposes an adversarial framework for handling imbalanced data.
problem Handling imbalanced data in classifier training.
method Adversarial approach to weight majority class samples.
result Boosts classifier performance on imbalanced data.
The paper classifies capillary graphs on manifolds with Ricci lower bounds.
problem Understanding capillary graphs on manifolds with Ricci lower bounds.
method Gradient estimate for positive CMC graphs on manifolds with Ricci lower bounds.
result Classification of capillary graphs over specific domains.
Paper tackles node injection attacks on graphs using reinforcement learning.
problem Tackles the problem of injecting adversarial nodes into real-world graph applications to reduce node classification performance.
method Uses reinforcement learning to sequentially modify the adversarial information of injected nodes.
result Demonstrates superior performance of the proposed method NIPA compared to existing methods.
Classifies spatial graphs with finite N-quandles.
problem Determining isomorphism of spatial graphs' N-quandles.
method Generalized N-quandles to spatial graphs, proving basic results and conjecturing a classification.
result Verifies conjecture in several cases, presents a possible counterexample.
New bounds for average graph distance using curvature and centrality.
problem Finding bounds for average graph distance.
method Using weighted average Ollivier curvature with edge betweenness centrality.
result Equality in bounds achieved for specific reflective graphs.
A new discrete formula connects vertex and edge distributions on graphs.
problem Optimal transport on graphs with mixed vertex and edge distributions.
method Discrete transport equation and Benamou-Brenier formulation.
result Classification of all Wasserstein-1 geodesics on graphs.
Graph ConvNet improves ncRNA classification accuracy.
problem Classifying non-coding RNA sequences into families.
method Graph Convolutional Network model trained on raw RNA graphs.
result 85.73% accuracy and 85.61% F1-score over 13 classes.
This paper classifies planar-Rips complexes and their unit disk graphs up to homotopy.
problem Classifying planar-Rips complexes and their unit disk graphs.
method Simplicial classification, homotopy equivalence, and hereditary properties.
result Classification of planar-Rips complexes and unit disk graphs up to homotopy.