New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.
problem Representing subgroups of surface groups in a combinatorial way.
method Introducing core surfaces as 2-dimensional complexes made up of vertices, labeled edges, and 4g-gons.
result Core surfaces are compact when corresponding subgroups are finitely generated.
A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
Recovering core nodes from graph data with missing fringe interactions.
problem Recovering the core set from graph data with missing fringe interactions.
method Developed a theoretical framework and algorithms based on fixed-parameter tractability.
result Our algorithms outperform existing methods on various real-world datasets.
New algorithm detects cores in graphs with community structure, improving vertex selection for better clustering.
problem Understanding and detecting core-periphery structures in graphs with community structure.
method Introduces relative centrality to detect cores in graphs with community and core-periphery structures.
result Relative centrality solves bias issues in core detection, leading to better vertex selection and improved clustering performance.
KCoreMotif clusters large networks efficiently by exploiting k-core decomposition and motifs.
problem Efficiently clustering large networks for trust evaluation.
method Exploits k-core decomposition and motifs to perform motif-based spectral clustering on k-core subgraphs.
result The proposed algorithm is accurate and efficient for large networks.
The paper develops formulas to count sizes of Markov equivalence classes of DAGs.
problem Measuring uncertainty and complexity in causal learning from DAGs.
method Introducing core graphs and deriving polynomial size formulas via symbolic computation.
result Efficient formulas for counting sizes of Markov equivalence classes of DAGs.
Surgery paths in sphere graph have limited distance.
problem Understanding distances between surgery paths in the sphere graph.
method Relied on understanding surgeries' effect on Guirardel core and equivalence to Rips moves.
result Hausdorff distance between any two surgery paths is at most 4.
CTGCN learns dynamic graph embeddings preserving both local and global graph structure.
problem Learning node representations for evolving graphs while preserving both local and global graph structure.
method CTGCN uses k-core based temporal graph convolutional network to learn dynamic graph embeddings.
result CTGCN outperforms existing methods in link prediction and structural role classification.
COREclust detects representative variables in high-dimensional data.
problem Detecting representative variables in high-dimensional data with limited observations.
method CORE-clustering algorithm detects CORE-clusters, variable sets with similar variables, and representative variables are estimated as CORE-cluster centers.
result The CORE-clustering algorithm can handle large datasets efficiently.
Recovering core nodes in hypergraphs from fringe interactions.
problem Recovering core nodes from fringe interactions in hypergraphs.
method Modeling core recovery as a hitting set problem in hypergraphs, developing a practical algorithm.
result Demonstrated the effectiveness of the algorithm on real-world datasets.
The paper tackles scalability issues in Graph Representation Learning.
problem Prohibitive time and memory complexities in Graph Representation Learning.
method Leveraging the K-Core Decomposition property of Graphs to reduce time and memory consumption.
result Proposed techniques significantly reduce computational resources without compromising embedding quality.
We develop spectral spanners for vectors and use them to create efficient core-sets for determinant maximization.
problem Maximizing determinants of vector sets.
method Spectral spanners and greedy algorithm.
result Almost optimal composable core-sets for determinant maximization.
By proving graph theoretical versions of Green-Stokes, Gauss-Bonnet and Poincare-Hopf, core ideas of undergraduate mathematics can be illustrated in a simple graph theoretical setting. In this pedagogical exposition we present the main proofs on a single page and add illustrations. While discrete Stokes is is old, the …
Link prediction benefits from fringe nodes in some datasets but not all.
problem Impact of fringe nodes on link prediction in core-fringe networks.
method Analysis of core-fringe network data and link prediction performance.
result The inclusion of fringe nodes can either improve or harm link prediction performance, depending on the dataset.
The paper studies graph products of groups and recovers graph and vertex groups under certain conditions.
problem Recovering graph and vertex groups from graph products of groups.
method Using non-generic almost positive sentences, the authors show that under specific conditions, the underlying graph and vertex groups can be recovered.
result The core of the defining graph determines an invariant of the elementary theory of a right-angled Artin group.
GSimCNN predicts graph similarity using CNNs, outperforming existing methods.
problem Challenging pairwise graph similarity computation due to NP-hardness.
method Graph Edit Distance (GED) as core metric, GSimCNN (Convolutional Neural Networks).
result State-of-the-art performance on graph similarity search.
Method learns software resource usage from snapshots.
problem Challenges in learning time-varying, correlated resource usage.
method Graph structured Schrödinger bridge problem for nonparametric learning.
result Predicts most-likely resource distributions.
A new method for neural network initialization using graph degeneracy.
problem Improving neural network performance through better initialization.
method Adapted k-hypercore decomposition for neural network initialization.
result k-hypercore outperforms state-of-the-art initialization methods.
NGE uses neural graphs to efficiently design robots.
problem Designing robots is hard due to combinatorial search space and evaluation costs.
method Formulated as graph search, NGE uses neural networks for policy parameterization and graph mutation with uncertainty.
result NGE significantly outperforms previous methods, discovering kinematically preferred structures.
P&C combines multiple perturbed graphs to improve influential spreader detection.
problem Ineffective algorithms are unstable to small network perturbations.
method Creates multiple perturbed graphs, applies scoring function to each, and combines results.
result P&C significantly improves influential spreader detection without extra cost.
Generative model creates new molecules retaining a scaffold with certainty.
problem Designing new molecules with a specific scaffold.
method Generative model that extends scaffold graph by adding vertices and edges.
result Model can generate novel molecules with high validity, uniqueness, and novelty.
Develops a hybrid model for text summarization.
problem Summarizing long text sequences concisely.
method Extends sequence encoders with a graph component to handle long-distance relationships in text.
result Hybrid models outperform pure sequence or graph models on summarization tasks.
New algorithm improves graph inference tasks.
problem Complex graph reasoning and prediction tasks.
method Policy Message Passing algorithm reformulates graph inference as stochastic sequential processes.
result Consistently outperforms state-of-the-art models.
Stable cylinders found in hyperbolic groups and curve graphs.
problem Torsionfree hyperbolic groups and curve graphs of surfaces have globally stable cylinders.
method Generalised Sageev's construction to improve fine properties of hyperbolic spaces.
result Proved curve graphs of surfaces admit equivariant quasi-isometric embeddings in finite products of quasitrees.
GraKeL combines multiple graph kernels for graph similarity measurement.
problem Accurately measuring graph similarity across various applications.
method Unified graph kernel library in Python with scikit-learn interface.
result Facilitates graph classification and clustering tasks.
New framework models graph signals as distribution-valued signals in Wasserstein space.
problem Limitations of classical vector-based GSP, including synchronous observations and uncertainty.
method Introduces graph distribution-valued signals (GDSs) in the Wasserstein space.
result GDSs naturally encode uncertainty and stochasticity, generalizing traditional graph signals.
Ring-reservoir networks simplify graph embeddings efficiently.
problem Efficient graph embeddings using deep neural networks.
method Progressive simplification of Reservoir Computing models to ring topology.
result Ring-reservoir networks show consistent advantages in predictive performance.
Surveying topological complexity of graph configurations, unifying traditional and modern approaches.
problem Understanding the topological complexity of configuration spaces of graphs.
method Exploring traditional cohomology methods and modern asphericity/fundamental group approaches.
result Unified understanding of topological complexity through both traditional and modern methods.
Study on modified Ricci curvature on graphs, proving rigidity and deriving formulas.
problem Understanding Ricci curvature on graphs, especially for specific graph types.
method Introduced modified Ricci curvature, established rigidity theorem, derived formulas for strongly regular graphs.
result Rigidity theorem for complete graphs and explicit formulas for strongly regular graphs.
Graph neural networks are vulnerable to adversarial attacks that manipulate graph structure.
problem Vulnerability of graph neural networks to adversarial attacks.
method Meta-learning approach to solve bilevel optimization problem of training-time attacks.
result Small graph perturbations can significantly degrade graph neural network performance.
A new method embeds sparse stochastic graphs into low dimensions.
problem Embedding large, sparse, stochastic graphs into low-dimensional spaces.
method Spaceland Embedding (SG-t-SNE) inspired by t-SNE, leveraging modern computing techniques.
result Effective embedding results on synthetic and real-world graphs.
Galerkin method outperforms graph-based methods in spectral decompositions.
problem Improving spectral decomposition methods in machine learning.
method Restricting study to a small set of test functions using the Galerkin method.
result Statistical and computational superiority of Galerkin method over graph-based approaches.
We prove a conjecture of Menasco and Zhang that if a tangle is completely tubing compressible then it consists of at most two families of parallel strands. This is related to problems of graphs in 3-manifold. A 1-vertex graph Γ in a 3-manifold M with a genus 1 Heegaard splitting is standard if it consists of one or…
Study minimal graphs on non-negative Ricci curvature manifolds.
problem Minimal graphs with linear growth on manifolds with non-negative Ricci curvature.
method New gradient estimate for minimal graphs and heat equation techniques.
result Non-constant minimal graphs force tangent cones to split off a line.
Mapper tool preserves graph structures for better visualization.
problem Graphs can be hard to visualize for large datasets.
method Developed a variation of mapper for weighted, undirected graphs.
result Homology-preserving skeletons enable multi-scale visualization.
Two embedding methods in spectral graph clustering yield different but valid groupings.
problem Clustering vertices of a graph without true groupings.
method Spectral graph clustering using Laplacian or Adjacency spectral embedding.
result Laplacian embedding captures left hemisphere/right hemisphere structure, while adjacency embedding captures gray matter/white matter structure.
New centrality-based graph shift operators improve graph neural networks.
problem Improving graph neural networks by enhancing graph shift operators.
method Proposed Centrality Graph Shift Operators (CGSOs) using global centrality metrics.
result CGSOs lead to improved performance in graph neural networks on real-world datasets.
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.
New method speeds up sparse graph neural networks training on dense hardware.
problem Training sparse graph neural networks is slow on custom hardware.
method Inspired by sparse matrix optimization, developed techniques for dense hardware.
result Sparse graph neural networks trained in 13 minutes on 512-core TPUv2 Pod.
Stochastic block model shows universal applicability to network inference problems.
problem Finding partitions in complex networks that maximize objective functions.
method Showed equivalence of popular algorithms to maximum likelihood formulation of SBM.
result SBM is nearly universal for solving MPE problems.
GWCA analyzes cross-graph correlations for movie retrieval.
problem Cross heterogeneous graph comparison in movie retrieval.
method Spectral graph filtering, Wasserstein metric learning, generalized eigenvalue decomposition.
result Surprise consistency in learning processes and closed-form solution.
Graph diffusion convolution improves graph learning by leveraging generalized graph diffusion.
problem Noisy and arbitrarily defined edges in real graphs.
method Graph diffusion convolution (GDC) using generalized graph diffusion like heat kernel and personalized PageRank.
result Replacing message passing with graph diffusion convolution leads to significant performance improvements.
A reinforcement learning algorithm improves graph construction for robustness.
problem Improving graph construction for specific objectives.
method Reinforcement learning and graph neural networks.
result The approach outperforms existing methods in robustness.
DMGNN predicts 3D human motions using adaptive multiscale graphs.
problem Predicting 3D skeleton-based human motions accurately.
method Dynamic multiscale graph neural networks (DMGNN) with adaptive multiscale graphs and MGCU.
result DMGNN outperforms state-of-the-art methods in short and long-term predictions.
R-GPM enables efficient graph pattern mining through user-defined relations.
problem Efficient graph pattern mining through user-defined relations.
method Parallel computing framework with MCMC sampling algorithm and optimizations.
result Efficient estimators for graph pattern statistics with up to 3-orders-of-magnitude computational cost reduction.
The bane of one-class collaborative filtering is interpreting and modelling the latent signal from the missing class. In this paper we present a novel Bayesian generative model for implicit collaborative filtering. It forms a core component of the Xbox Live architecture, and unlike previous approaches, delineates the o…
GTNs learn new graph structures and improve node representation learning.
problem Learning node representations on misspecified or heterogeneous graphs.
method Graph Transformer Networks (GTNs) that generate new graph structures and learn effective node representations.
result GTNs achieve state-of-the-art performance in node classification tasks without predefined meta-paths.
Paper introduces new graph concepts for better modeling of temporal interactions.
problem Graph theory struggles to capture temporal and structural aspects of interactions.
method Generalizes graph concepts to handle both temporal and structural aspects of interactions.
result Formalism allows direct modeling of interactions over time, similar to graph theory.