New discrete surface theory defined for 3D graphs.
problem No corresponding smooth surfaces for discrete surfaces.
method Defined Gauss and mean curvature for 3-valent graphs.
result Discrete surfaces converge to smooth surfaces in limit.
We give a generalization of Fukaya's Morse homotopy theoretic approach for 2-loop Chern--Simons perturbation theory to 3-valent graphs with arbitrary number of loops at least 2. We construct a sequence of invariants of integral homology 3-spheres with values in a space of 3-valent graphs (Jacobi diagrams or Feynman dia…
A theory of complexity for pairs (M,G) with M an arbitrary closed 3-manifold and G a 3-valent graph in M was introduced by the first two named authors, extending the original notion due to Matveev. The complexity c is known to be always additive under connected sum away from the graphs, but not always under connected s…
A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigz…
New topological realization of Kontsevich graph complex for large dimensions.
problem Understanding the rational homotopy groups of Diff partial(D2k).
method Construction of a chain map from Kontsevich graph complex to rational singular chain complex.
result New elements in rational homotopy groups of BDiff partial(D2k) determined by cycles in graph complex.
The aim of this paper is to classify simply connected 6-dimensional torus manifolds with vanishing odd degree cohomology. It is shown that there is a one-to-one correspondence between equivariant diffeomorphism types of these manifolds and 3-valent labelled graphs, called torus graphs introduced by Maeda-Masuda-Panov. …
We formulate a conjecture (already proven by A. Kricker) about the structure of Kontsevich integral of a knot. We describe its value in terms of the generating functions for the numbers of external edges attached to closed 3-valent diagrams. We conjecture that these functions are rational functions of the exponentials …
We study 3-valent maps Mn(p,q) consisting of a ring of n q-gons whose the inner and outer domains are filled by p-gons, for p,q≥3. We describe a domain in the space of parameters p, q, and n, for which such a map may exist. With four infinite sequences of maps - prisms Mp(p≥3,4), $M_4(4,q \g…
Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
problem Limited theoretical understanding of line graph transformation's impact on GNN models.
method Examined CFI and strongly regular graphs, showing line graph transformation helps WL tests distinguish these graphs.
result Line graph transformation aids WL tests in distinguishing challenging graph properties.
Proposes MGMN for end-to-end graph similarity learning.
problem Lack of cross-level interactions in graph similarity learning.
method Multi-level graph matching network (MGMN) combining node-graph matching and siamese graph neural networks.
result MGMN outperforms state-of-the-art models on graph-graph classification and regression tasks.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
edGNN improves graph embeddings for directed labeled graphs.
problem Improving node and graph embeddings for directed labeled graphs.
method edGNN is a GNN designed for directed labeled graphs, leveraging both topology and labels.
result edGNN is as powerful as the Weisfeiler-Lehman algorithm for graph isomorphism.
Graph CNNs adapt to varying graph structures for better performance.
problem Fixed graph structures limit the performance of Graph CNNs on real data.
method Adaptive graph learning and distance metric learning for efficient graph construction.
result Adaptive Graph CNNs improve convergence speed and predictive accuracy on various graph datasets.
MxPool learns graph features from diverse graphs using a hierarchical structure.
problem Learning graph features from diverse graphs with varying properties and sizes.
method MxPool uses a multiplex structure with multiple graph convolution/pooling networks in a hierarchical learning structure.
result MxPool outperforms state-of-the-art methods on graph classification benchmarks.
Study the geometry of graph product extension graphs.
problem Properties of graph products.
method Introduce and study the extension graph of graph products of groups.
result Extension graph is isomorphic to crossing graph of a quasi-median graph and exhibits asymptotic dimension similar to quasi-trees.
Graph neural network learns graph distances effectively.
problem Maintaining graph distance metric properties.
method GRAPH-BERT based semi-supervised distance metric learning.
result GB-DISTANCE outperforms existing methods.
UGRAPHEMB embeds graphs into vectors preserving their proximity, achieving competitive results.
problem Graph-level representation learning in an unsupervised and inductive manner.
method UGRAPHEMB uses graph-graph proximity to embed graphs into a vector space. MSNA generates multi-scale node attention for graph-level embedding.
result UGRAPHEMB achieves competitive accuracy in graph classification, similarity ranking, and visualization tasks.
Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
problem Quasi-transitive graphs quasi-isometric to planar graphs need to be upgraded to Cayley graphs.
method Upgrading a planar graph to a Cayley graph.
result Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.
Deep Divergence Graph Kernels learn graph representations without supervision.
problem Learning graph representations without feature engineering or labeled graphs.
method Unsupervised method using cross-graph attention networks and divergence scores.
result Learned representations achieve competitive results on graph classification tasks.
Paper proposes a new graph embedding framework to improve graph analytics.
problem Graph embedding often fails to capture the distribution of latent codes.
method Adversarial graph autoencoder framework that combines topological structure and node content.
result ARGA and ARVGA outperform baselines in link prediction, clustering, and visualization.
GRAPH-BERT uses only attention for graph representation learning.
problem Graph neural networks over-rely on graph links and suffer from performance issues.
method GRAPH-BERT uses only attention mechanism without graph convolution or aggregation, trained on sampled subgraphs.
result GRAPH-BERT outperforms existing GNNs in learning effectiveness and efficiency.
Customized-GNN generates model-specific for each graph.
problem Graphs in the same dataset have distinct structures.
method Proposes Customized-GNN framework to generate model-specific for each graph.
result Demonstrates effectiveness on various graph classification benchmarks.
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.
Graph ConvNets outperform RNNs in graph learning tasks.
problem Designing neural networks for graphs with variable length.
method Compare graph RNN and ConvNet architectures, propose extensions, and conduct controlled experiments.
result Graph ConvNets are more accurate and faster than graph RNNs.
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.
HGP-SL pools and learns graph structure for hierarchical representation learning.
problem Graph pooling is overlooked in GNN models, limiting hierarchical representation learning.
method Integrates graph pooling and structure learning into a unified module.
result HGP-SL improves graph classification performance on benchmarks.
The paper shows conflict graphs of Petersen family graphs are mostly unbalanced.
problem Understanding the balance of conflict graphs in Petersen family graphs.
method Analyzing maximally planar subgraphs and their conflict graphs.
result All but three strong conflict graphs from Petersen Family Graphs are unbalanced.
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.
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.
We define a pseudo-inverse for line graphs using linear integer programming.
problem Not all graphs have a corresponding root graph, making the line graph operation non-invertible.
method Propose a linear integer program to edit the smallest number of edges in the line graph to recover a root graph.
result The pseudo-inverse operation is well-behaved and works in practice as shown by empirical experiments.
Dual-Primal Graph CNN learns vertex and edge features on graphs.
problem Learning features on non-Euclidean structured data like graphs.
method Alternates graph convolutional operations on graph and its dual.
result State-of-the-art results on various graph benchmarks.
HaarPooling compresses graphs by Haar transforms, improving graph classification and regression.
problem Handling graphs of varying size and structure in GNNs.
method HaarPooling, a cascade of clusterings and compressive Haar transforms.
result HaarPooling synthesizes graph features into uniform size, achieving state-of-the-art performance.
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.
RL-VAE uses RL to decode molecular graphs from latent embeddings.
problem Efficiently decoding molecular graphs from latent embeddings.
method Repurposed simple graph generator for efficient decoding.
result Decoding molecular graphs from latent embeddings is possible with a simple graph generator.
Develops method to create non-Abelian Ricci-flat graphs via bundles.
problem Creating non-Abelian Ricci-flat graphs.
method Develops systematic way via graph bundles with constraints.
result Non-trivial graph bundles are not isomorphic to product of base and fiber.
MathNet uses wavelets for graph representation and learning.
problem Graph Neural Networks (GNNs) for graph classification and regression.
method Multiresolution Haar-like wavelets, graph convolution, and pooling.
result MathNet achieves notable accuracy gains on graph classification and regression tasks.
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.
New method uses graph generative models for graph classification.
problem Graph classification for non-relational i.i.d. data.
method Derive classification formulas from GGM, train generative graph auto-encoder model.
result New conditional ELBO for training graph auto-encoder model.
Unified framework for graph coarsening using node features and graph matrices.
problem Dimensionality reduction of large graphs while preserving node features.
method Optimization-based framework that unifies graph learning and dimensionality reduction.
result The learned coarsened graph is ε-similar to the original graph, where ε is a small positive number.
Simple graph representation outperforms complex methods in graph classification.
problem Graph classification and representation learning on graphs.
method Developed a simple yet meaningful graph representation and tested its effectiveness.
result Simple graph representation achieves similar performance to state-of-the-art methods for non-attributed graph classification.
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.
Graph Laplacian spectrum serves as a robust feature representation.
problem Difficulties in analyzing and comparing graphs due to their structure.
method Proposes using the graph Laplacian spectrum (GLS) as a feature representation.
result Graph Laplacian spectrum (GLS) preserves structural information and is consistent under deformation and invariance under isomorphism.
PSimGNN partitions graphs into subgraphs for efficient graph similarity computation.
problem Efficiently compute graph similarity scores for large graphs.
method Graph partitioning followed by subgraph-level and node-level comparisons using a graph neural network.
result PSimGNN outperforms state-of-the-art methods in graph similarity computation tasks.
Paper proposes a novel adversarial framework for graph embedding.
problem Graph embedding often fails to represent latent codes effectively.
method Adversarial training to enforce latent codes to match a prior distribution.
result ARGA and ARVGA models improve graph embedding for link prediction and clustering.
ARMA graph filters approximate any graph frequency response and are stable in time-varying settings.
problem Designing efficient graph filters for signals on graphs.
method Autoregressive moving average (ARMA) recursions for graph filtering.
result ARMA graph filters can approximate any desired graph frequency response and are stable in time-varying settings.
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.
This paper develops graph theory for racks and quasigroups.
problem Characterizing and realizing right quasigroups and related structures.
method Study of graph markings, Schreier graphs, and Cayley graphs.
result All right quasigroups are realizable by specific types of graphs.