GCNs perform well on heterophilous graphs under certain conditions.
problem The necessity of homophily for good GNN performance.
method Empirical evaluation and theoretical analysis of GCNs on heterophilous graphs.
result GCNs can achieve strong performance on heterophilous graphs under certain conditions.
Causal inference improves heterophilic graph learning.
problem Capturing asymmetric node dependencies in graph learning.
method Intervention-based causal inference for graph structure learning.
result CausalMP achieves superior link prediction performance.
GraphACL learns graph representations without augmentation or homophily assumptions.
problem Learning graph representations on heterophilic graphs (nodes with different labels and features).
method Asymmetric Contrastive Learning for Graphs (GraphACL) considers an asymmetric view of neighboring nodes.
result GraphACL significantly outperforms state-of-the-art methods on both homophilic and heterophilic graphs.
ES-MLP combines Graph-MLP with edge splitting for node classification on both homophilic and heterophilic graphs.
problem Node classification on graphs with mixed homophilic and heterophilic properties.
method Combines Graph-MLP with edge splitting mechanism from ES-GNN to learn two adjacency matrices based on relevant and irrelevant feature pairs.
result ES-MLP achieves performance comparable to homophilic and heterophilic models without using edges during inference.
New p-Laplacian GNN model tackles heterophilic graphs by improving node classification.
problem Heterophilic graphs where node labels differ, leading to poor GNN performance.
method Proposes p-Laplacian GNN model with a new message passing mechanism derived from discrete regularization. result Significantly outperforms state-of-the-art GNNs on heterophilic benchmarks.
ECGs improve GNNs for non-homophilic data.
problem Improving GNNs for datasets where nodes are not likely to belong to the same class.
method ECGs rewire GNNs' computation graph to connect nodes likely in the same class using weaker classifiers.
result ECGs improve GNN performance on non-homophilic datasets.
A new method boosts graph neural networks by preventing over-smoothing and over-squashing.
problem Graph Neural Networks struggle with long-range signals and over-smoothing/over-squashing.
method Proposes PowerEmbed, a layer-wise normalization technique inspired by spectral graph embedding.
result PowerEmbed prevents over-smoothing and avoids over-squashing, improving performance on heterophilous graphs.
SCNode improves node embeddings for GNNs in both homophilic and heterophilic graphs.
problem Challenges in node representation quality and generalization in GNNs, especially in heterophilic graphs.
method SCNode integrates spatial and contextual information to create more discriminative and structurally aware node embeddings.
result SCNode achieves superior performance over conventional GNN models on benchmark datasets.
GNNs generalize better on homophilic graphs than heterophilic ones.
problem Understanding the generalization error of GNNs on graph data.
method Analytical tools from statistical physics and random matrix theory.
result Risk is shaped by graph noise, feature noise, and training labels.
Heterophily affects GNN robustness; separating ego- and neighbor-embeddings improves defense.
problem The robustness of GNNs to adversarial attacks.
method Formalized relation between heterophily and GNN robustness; empirical analysis; design principles for improved robustness.
result Separating ego- and neighbor-embeddings increases GNN robustness.
Graph convolutional deep kernel machine learns representations for graph tasks.
problem Limited representation learning in infinite-width neural networks.
method Developed a graph convolutional deep kernel machine as an infinite-width limit.
result Representation learning improves performance for heterophilous node classification tasks.
The p-Laplacian Transformer improves transformer models by assigning higher attention weights to tokens in close proximity.
problem The self-attention mechanism in transformers does not effectively distinguish attention weights between tokens in close and non-close proximity.
method Proposes a novel class of transformers, p-Laplacian Transformers, that use p-Laplacian regularization to assign higher attention weights to tokens in close proximity. result Empirically demonstrates that p-Laplacian Transformers outperform baseline transformers on various benchmark datasets.
Graph convolutions can enhance high frequencies, leading to over-sharpening.
problem Graph convolutions suffer from over-smoothing and poor performance on heterophilic graphs.
method Rigorously prove that linear graph convolutions minimize a generalized Dirichlet energy, showing that weight matrices induce edge-wise attraction or repulsion.
result Graph convolutions can enhance high frequencies, leading to over-sharpening instead of over-smoothing.
Spectro-Riemannian Graph Neural Networks integrate spectral and curvature signals for better graph representation learning.
problem Enhance graph representation learning by leveraging spectral and curvature signals.
method Proposes Spectro-Riemannian Graph Neural Networks (CUSP) that combines spectral and curvature insights.
result Empirical evaluation shows CUSP outperforms state-of-the-art models by up to 5.3%.
Adaptive GPR-GNN optimizes node feature and topology learning.
problem Optimizing GNNs for both node features and graph topology, regardless of homophily or heterophily.
method Adaptive Universal Generalized PageRank (GPR) Graph Neural Network (GPR-GNN) that learns optimal GPR weights.
result Significant performance improvement on node classification tasks compared to state-of-the-art GNNs.
Graph neural networks are explained through energy gradient flow and framelet decomposition.
problem Understanding and improving graph neural networks.
method Viewing framelet-based models as gradient flows of energy, proposing a generalized energy via framelet decomposition.
result The proposed model leads to more flexible dynamics, enhancing graph neural networks.
Gradient Gating improves deep GNNs by modulating message passing updates.
problem Oversmoothing and performance degradation in deep GNNs.
method Gradient gating mechanism for multi-rate message passing.
result G2 framework alleviates oversmoothing and achieves state-of-the-art performance. New method handles structural uncertainty in graphs better than existing models.
problem Handling heterophily and structural noise in semi-supervised learning on graphs.
method Sparse signed message passing network that models a posterior distribution over signed adjacency matrices.
result Our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise.
GCNs learn by embedding similar nodes within a class and leveraging consistent neighborhood structures.
problem Understanding how GCNs perform semi-supervised node classification on both homophilous and heterophilous graphs.
method Investigated the latent node embeddings and neighborhood structures of GCNs.
result GCNs learn by embedding similar nodes within a class and leveraging consistent neighborhood structures.
Graph pruning improves neural network performance by addressing squashing and smoothing issues.
problem Over-squashing and over-smoothing in Graph Neural Networks.
method Proposes edge deletions to simultaneously address over-squashing and over-smoothing, optimizing spectral gap.
result Edge deletions improve generalization and distinguishability of nodes of different classes.
Graph Cascades rewire graphs to improve structure-aware learning.
problem Improving graph neural networks and transformers for structure-aware learning.
method Graph Cascades uses contagion-based diffusion processes to construct an auxiliary graph with reinforced edges.
result Graph Cascades improves node-classification benchmarks across various graph types.
The paper explores how different patterns of heterophily affect Graph Neural Networks.
problem Understanding the impact of heterophily on Graph Neural Networks.
method Theoretical analysis and experiments with Heterophilous Stochastic Block Models (HSBM).
result The impact of heterophily on classification depends on the Euclidean distance of neighborhood distributions and the averaged node degree.
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow interpretation of those vector representations as latent position estimates. The general…
Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on node-wise classification, illustrated with community detection on stochastic block m…
New method for directed graphs using learnable spectral positional encodings.
problem Challenges in magnetic Laplacians and unitary gauge invariance for directed graphs.
method Learnable spectral PEs of the form hθ(Aq)R, computed in Hermitian block Krylov subspace.
result Gauge-invariant and computationally efficient solution for directed graphs.
A new method for spectral positional encodings in directed graphs using Hermitian block Krylov subspaces.
problem Challenges in spectral positional encodings for directed graphs, including computational complexity and gauge invariance issues.
method Learnable spectral positional encodings of the form hθ(Aq)R, computed in a Hermitian block Krylov subspace from sparse matrix-vector products. result The method is gauge-invariant and converges to the exact eigendecomposition oracle as the depth grows.
PolyNSD improves Neural Sheaf Diffusion with polynomial operators and spectral rescaling.
problem Limitations of common Neural Sheaf Diffusion implementations, including scalability and stability issues.
method Introduces Polynomial Neural Sheaf Diffusion (PolyNSD) with a degree-K polynomial propagation operator and spectral rescaling.
result PolyNSD achieves state-of-the-art results on both homophilic and heterophilic benchmarks with reduced runtime and memory requirements.
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these "intermediate fusion" methods involve obtaining a low column rank matr…
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Quadratic bounds found for graph dimensions.
problem Understanding dimensions of arc and disk graphs.
method Quadratic upper bounds calculation.
result Asymptotic dimensions of arc and disk graphs have been bounded.
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.
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.