A fast graph embedding method for large graphs.
problem Efficiently embedding large graphs for various applications.
method One-hot graph encoder embedding with linear complexity.
result Graph encoder embedding is approximately normally distributed and converges to its mean.
Well-quasi-orders proved on embedded planar graphs.
problem Proving well-quasi-orders on embedded planar graphs.
method Careful analysis and extensions of classical methods for embedded minor relations.
result Embedded minor relations are well-quasi-orders on various classes of embedded planar graphs.
Two new methods improve graph embedding without needing a complete graph structure.
problem Graph autoencoders' performance depends on the adjacency matrix quality.
method BAGE and VBAGE: unsupervised graph embedding via adaptive graph learning.
result The methods expand GAEs' applicability to datasets without graph structure.
Curvature regularization prevents distortion in graph embeddings.
problem Graph topology patterns distort in Euclidean space, making detection difficult.
method Proposes curvature regularization to enforce flatness in embedding manifolds.
result Significant improvements in five embedding methods on open graph datasets.
Paper proposes a novel graph recovery attack from node embeddings.
problem Privacy risks of integrating graph embeddings with machine learning pipelines.
method Model-agnostic graph recovery attack exploiting preserved structural information in node embeddings.
result Adversaries can recover graph edges with decent accuracy from node embeddings alone.
A new method for fast graph embedding using diffusion graphs.
problem Efficiently generating graph embeddings for large networks.
method Diffusion graphs for rapid vertex sequence generation.
result Improved accuracy and performance with higher edge density.
We announce results about flat (linkless) embeddings of graphs in 3-space. A piecewise-linear embedding of a graph in 3-space is called {\it flat} if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the compleme…
There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedd…
GLACE embeds large-scale attributed graphs effectively, preserving structure and attributes.
problem Uncertainty and complexity in large-scale attributed graphs.
method Gaussian embeddings for scalable and efficient graph embedding.
result GLACE outperforms state-of-the-art methods on multiple graph analysis tasks.
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not scale well to large graphs. We therefore propose a framework for parallel computat…
Efficiently computes embeddings for large graphs using coarsening.
problem Inefficient computation of graph embeddings for large-scale graphs.
method Graph coarsening based on Schur complements and Gaussian elimination.
result Efficiently computed embeddings on coarsened graph match Schur complement embeddings in expectation.
A new framework for knowledge graph embedding using sheaves.
problem Learning representations for entities and relations in knowledge graphs.
method Using cellular sheaves to describe knowledge graph embeddings with consistency constraints.
result A generalized framework for reasoning about knowledge graph embedding models.
WEGL embeds graphs in a vector space for faster machine learning.
problem Efficiently embedding graphs for machine learning tasks.
method Wasserstein distance for node embedding similarity, Monge maps for graph representation.
result State-of-the-art classification performance with superior computational efficiency.
Two graph homologies help compute embedding space.
problem Computing the rational homotopy group of long embeddings.
method Invented two graph homologies and constructed a map between them.
result A monomorphism from top hairy graph homology to top BCR graph homology.
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques aim to automatically create a low-dimensional representation of a given graph, whi…
Graphs embeddable on torus and linklessly in 3D can be embedded linklessly in standard torus.
problem Embedding linklessly in a standard torus for graphs embeddable on torus and in 3D.
method Analyzing graphs of order 9 and below, showing linkless embedding in standard torus.
result For graphs of order 9 and below, linkless embedding in standard torus is possible.
New sampling methods improve node embedding efficiency.
problem Efficiency and scalability in node embedding methods.
method Sampling approaches to node embedding, modeling eigenvectors and feature vectors.
result Improved computational efficiency and scalability.
Characterizes graphs with leveled embeddings and introduces new graph invariants.
problem Understanding the properties of leveled embeddings in spatial graphs.
method Characterization of graphs with leveled embeddings, introduction of new invariants.
result Characterization of graphs with low level number and determination of specific invariants for complete graphs and complete bipartite graphs.
Solves Skopenkov's problem on graph embedding criteria.
problem Criteria for toroidal embedding of one-vertex ribbon graphs.
method Analyzes one-vertex ribbon graphs with additional disc structure.
result Provides solutions to Skopenkov's problem.
The study evaluates memory and capacity of graph embedding methods.
problem Assessing the memory and capacity of graph embedding methods.
method Not specified in the abstract provided.
result Not specified in the abstract provided.
Graph embedding leaks sensitive graph properties and subgraphs.
problem Privacy risks in graph embedding sharing.
method Three inference attacks and a defense mechanism.
result High accuracy in inferring graph properties and subgraphs.
Landmark-based node embeddings approximate shortest path distances in random graphs.
problem Capturing global graph distances in node representations.
method Landmark-based node embeddings using shortest path distances from a subset of reference nodes (landmarks).
result Random graphs require lower dimensions in landmark-based embeddings compared to worst-case graphs.
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency structure on the half-edges around each vertex, and an embedding of a *-graph is…
A graph embedded in the 3-sphere is called irreducible if it is non-splittable and for any 2-sphere embedded in the 3-sphere that intersects the graph at one point the graph is contained in one of the 3-balls bounded by the 2-sphere. We show that irreducibility is preserved under certain deformations of embedded graphs…
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…
Paper proposes KE-GCN for better graph embedding.
problem Efficiently leveraging complex graphs with heterogeneous entities and relations.
method Combines GCNs and knowledge embedding methods.
result Advantages in knowledge graph alignment and entity classification.
Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-B…
Enhances graph classification with multiple graphs.
problem Improving graph classification accuracy with multiple graphs.
method Graph fusion embedding using encoder embedding.
result The method consistently improves classification accuracy for large vertex sets.
Graph embedding techniques have been increasingly deployed in a multitude of different applications that involve learning on non-Euclidean data. However, existing graph embedding models either fail to incorporate node attribute information during training or suffer from node attribute noise, which compromises the accur…
With the great success of graph embedding model on both academic and industry area, the robustness of graph embedding against adversarial attack inevitably becomes a central problem in graph learning domain. Regardless of the fruitful progress, most of the current works perform the attack in a white-box fashion: they n…
Algorithm calculates genus of embedded graphs on surfaces.
problem Finding minimal and maximal genus for graph embeddings.
method Constructing special branched coverings of the 2-sphere.
result Algorithm calculates orientable genus and maximal genus of graphs.
Introduces PELP for graph-enhanced word embeddings.
problem Combining graph side-information into static word embeddings.
method Probabilistic embeddings using Laplacian priors.
result Unified and flexible approach to various embedding methods.
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
problem Finding a surface embedding for general spatial graphs is not always possible.
method Define leveled property, decompose graph into subgraphs, and construct surface.
result For leveled spatial graphs with a small number of levels, a surface can always be found.
DAOR efficiently embeds graphs without tuning, improving speed and interpretability.
problem Graph embedding limitations in resource usage, interpretability, and parameter dependence.
method DAOR uses community detection to produce robust, interpretable embeddings without manual tuning.
result DAOR outperforms state-of-the-art techniques on node classification and link prediction.
Extends graph encoder embedding to weighted graphs and matrices.
problem Classifying vertices in various graph types efficiently.
method Graph encoder embedding applied to weighted graphs, distance matrices, and kernel matrices.
result The method achieves asymptotic normality, enabling optimal classification.
Proposes cone embedding for better graph hierarchical structure representation.
problem Lack of natural and interpretable hierarchical indicators in graph embeddings.
method Metric cone embedding method to capture hierarchical structure.
result Extracts hierarchical structure from other graph embedding outputs.
We study some graphs associated to a surface, called k-multicurve graphs, which interpolate between the curve complex and the pants graph. Our main result is that, under certain conditions, simplicial embeddings between multicurve graphs are induced by π1-injective embeddings of the corresponding surfaces. We also p…
Learning powerful data embeddings has become a center piece in machine learning, especially in natural language processing and computer vision domains. The crux of these embeddings is that they are pretrained on huge corpus of data in a unsupervised fashion, sometimes aided with transfer learning. However currently in …
New graph kernel scales well with graph size and number, achieving state-of-the-art performance.
problem Graph kernels lose structure information when representing graphs.
method Proposes a positive-definite global alignment graph kernel using random features and random graph embeddings.
result Achieves quasi-linear scalability with respect to graph size and number.
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.
AGE improves graph embedding by smoothing features and iteratively enhancing node embeddings.
problem Challenges in attributed graph embedding, especially in preserving optimal low-pass characteristics and robustness.
method AGE, a novel framework combining Laplacian smoothing and adaptive encoding, addresses these issues.
result AGE consistently outperforms state-of-the-art methods on node clustering and link prediction tasks.
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the jo…
IDGL learns better graph structure and embeddings iteratively.
problem Improving graph neural network node embeddings and graph structure.
method Iterative Deep Graph Learning framework that dynamically stops when graph structure optimizes for downstream tasks.
result IDGL consistently outperforms state-of-the-art baselines on nine benchmarks.
Framework for dynamic node embeddings from graph streams.
problem Temporal prediction-based applications using graph stream data.
method ε-graph time-series representation, temporal reachability graphs, weighted temporal summary graphs.
result Dynamic embedding methods achieve better predictive performance.
Low-dimensional embeddings of knowledge graphs and behavior graphs have proved remarkably powerful in varieties of tasks, from predicting unobserved edges between entities to content recommendation. The two types of graphs can contain distinct and complementary information for the same entities/nodes. However, previous…
Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the reconstruction errors for graph data. They have mostly overlooked the embedding dis…
APGE protects graph node representations from inference attacks.
problem Privacy leakage in graph embedding methods.
method Adversarial training framework with disentangling and purging mechanisms.
result APGE preserves structural and utility attributes while concealing private information.
The paper introduces a method for detecting principal communities and embedding vertices.
problem Detecting and embedding vertices in graphs with community structure.
method Principal graph encoder embedding method that detects principal communities and produces vertex embeddings.
result The method successfully detects principal communities and produces accurate vertex embeddings.