New method for faster graph parameter inference from large random Kronecker graphs.
problem Efficiently infer graph parameters from large random Kronecker graphs.
method Decompose adjacency matrix into signal and noise components, then use denoising and solving approach.
result Proposed method achieves comparable or better performance than existing methods at lower computational cost.
Graph Neural Networks struggle on random graphs without node identifiers.
problem Graph Neural Networks' limitations on random graphs without node identifiers.
method Study of Graph Neural Networks and Structural Graph Neural Networks convergence on large random graphs.
result Structural Graph Neural Networks are more powerful and universal than Graph Neural Networks on random graphs.
GCNs converge and remain stable on large random graphs, revealing geometric insights.
problem Understanding the behavior of GCNs on large, sparse random graphs.
method Analysis of GCNs on random graph models with latent variables and geometric edge probabilities.
result GCNs converge to their continuous counterparts as graph size increases, and are stable to small graph deformations.
New model preserves graph structure in large datasets.
problem Lack of permutation invariance in graph generation models for large graphs.
method Uses graph embeddings to create a scalable generative model.
result Model maintains structure in large graphs without losing invariance.
This paper evaluates LLMs on large graph property estimation tasks.
problem Limited context length of LLMs limits their evaluation on large graphs.
method Developed EstGraph dataset and introduced four tasks for LLMs to estimate large graph properties.
result LLMs perform better on graph property estimation tasks when provided with context-rich prompts based on random walks.
New sampling method for graph signals using DPPs for perfect recovery on small graphs, and sub-optimal but faster approach for large graphs.
problem Sampling k-bandlimited signals on graphs efficiently.
method Determinantal Point Processes (DPP) for both small and large graphs.
result Preliminary experiments show efficient sampling especially for graphs with strong community structure.
The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.
problem The size of Markov equivalence classes under relaxed assumptions.
method Analytical proofs for three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.
result Exponentially large lower bounds for the expected size of Markov equivalence classes.
Paper analyzes spectral clustering for large graphs using random signals.
problem Complex eigen decomposition for large graphs.
method Graph filtering of random signals for approximate spectral embedding.
result Consistency of spectral clustering in stochastic block model.
This paper explores GNN functions on random graphs, highlighting the importance of node Positional Encodings.
problem Understanding the expressive power of GNNs on large random graphs.
method General convergence notions, input node features, and Positional Encodings (PEs).
result GNNs can converge to certain functions on large random graphs, emphasizing the role of PEs.
New model calculates logarithmic surface diameter.
problem Calculating diameter of random hyperbolic surfaces.
method Exploration process inspired by graph breadth-first search.
result Diameter is logarithmic in surface genus.
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.
Develops graph kernels using random walk return probabilities.
problem Quantifying similarities among graphs.
method Graph kernels based on return probabilities of random walks.
result Significantly outperform existing graph kernels in accuracy and efficiency.
Random surfaces with long systoles created from graph theory ideas.
problem Finding surfaces with long systoles.
method Two constructions inspired by graph theory.
result Proved a new lower bound on systole length.
Study on convergence of graph neural networks on random graphs.
problem Convergence of message passing graph neural networks on large random graphs.
method Extended convergence results to a broad class of aggregation functions using McDiarmid inequality.
result Non-asymptotic bounds for convergence quantified with high probability.
A scalable framework for clustering large graphs using randomized sketching.
problem Clustering large partially observed graphs efficiently.
method Randomized graph sketching, correlation-based retrieval, uniform and degree-based node sampling.
result Improved phase transitions for clustering with reduced computational complexity and minimum cluster size.
New method for efficient ERG fitting on large graphs.
problem Fitting non-trivial ERGs on large graphs.
method Fast matrix block-approximation techniques for dyadic independence.
result Models can generate networks with similar properties to observed networks.
Uniform drift estimates found for random walks on graph products.
problem Finding uniform lower bounds on drift for random walks on graph products.
method Extending Gouëzel's argument and introducing the combinatorial notion of piling.
result Uniform lower bounds on the drift for a family of random walks on graph products.
Survey on statistical inference methods for random dot product graphs.
problem Statistical inference on random dot product graphs.
method Spectral embeddings of adjacency and Laplacian matrices.
result Consistency and asymptotic normality of spectral embeddings.
Linear time algorithm for random walk kernels on sparse graphs.
problem Efficient computation of general random walk kernels for large graphs.
method Sample dependent random walks to compute graph embeddings without direct graph product.
result Up to 27x faster and scalable to 128x larger graphs than previous methods.
GraphSAC detects anomalies in large graphs by sampling and filtering node subsets.
problem Vulnerability of holistic anomaly detection methods to compromised nodal attributes and network links.
method Randomly draws subsets of nodes, filters out contaminated sets, and uses SSL to estimate nominal label distributions.
result GraphSAC provides performance guarantees and is scalable to large graphs.
A test for comparing large random graphs based on network statistics.
problem Comparing friendship networks on Facebook and LinkedIn.
method General principle for two-sample hypothesis testing based on concentration of network statistics.
result A consistent two-sample test that is minimax optimal for certain network statistics.
SASE improves attributed graph clustering for large graphs with linear time and space complexity.
problem Challenges in clustering large attributed graphs due to high computational and memory costs.
method SASE combines node features smoothing, scalable spectral clustering, and adaptive order selection.
result SASE achieves a 6.9% improvement in ACC and a 5.87x speedup on the ArXiv dataset.
We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic blo…
New method learns node features from attributed graphs without node identity constraints.
problem Learning useful node features from attributed graphs for various tasks.
method Inductive representation learning using attributed random walks.
result Generalizes existing methods and supports large graphs.
Study of lengths of cycles in large genus random maps converging to Poisson process.
problem Understanding the distribution of cycle lengths in large genus random maps.
method Teichmüller theory approach for uniformly random metric maps (ribbon graphs).
result The length spectrum converges to a Poisson point process with an explicit intensity as genus tends to infinity.
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…
Estimates spectral density of large implicit matrices efficiently.
problem Estimating eigenvalues of large implicit matrices efficiently.
method Combines randomized estimation techniques to construct unbiased estimators.
result Validated methods on large-scale problems in graph theory and random matrix theory.
dynnode2vec embeds dynamic networks efficiently.
problem Capturing evolving patterns in large dynamic networks.
method dynnode2vec: a random walk based method initialized with previous embedding vectors.
result Demonstrates advantages over static methods on large dynamic network datasets.
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing some particular network properties (such as degree distribution or clustering coe…
A novel algorithm for unbiased graph kernel estimation with subquadratic time complexity.
problem Efficient estimation of graph kernels for large networks.
method Random walk-based algorithm with modulation function parameterized by neural network.
result Higher-quality kernel estimates and efficient scalable learning on larger networks.
Study finds root vertex in large networks with high probability.
problem Finding the root vertex in large growing networks.
method Constructs confidence sets for the root vertex in various random network models.
result Confidence sets of size independent of the number of vertices contain the root vertex with high probability.
SHAKE-GNN scales GNNs for large graphs with multi-scale representations.
problem Scaling Graph Neural Networks (GNNs) to large graphs.
method SHAKE-GNN uses a hierarchy of Kirchhoff Forests for stochastic multi-resolution graph decompositions.
result SHAKE-GNN achieves competitive performance on large-scale graph classification benchmarks.
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary pot…
Graph autoencoders improve node embeddings using random walk regularization.
problem Graph autoencoders' reconstruction loss ignores latent representation distribution.
method Random walk regularization to improve latent representations.
result The method achieves state-of-the-art accuracy on link prediction tasks.
Study on connectivity and geometry of random Coxeter groups.
problem Connectivity threshold for square percolation on random graphs.
method Probabilistic combinatorics and techniques from geometric group theory.
result Determines connectivity threshold and cubical coarse median structure for random Coxeter groups.
Improved algorithm for causal structure learning in large networks.
problem Estimating high-dimensional directed acyclic graphs from noisy data.
method A modified PC-Algorithm that uses small sets of variables for conditioning.
result Significant gains in computational complexity and estimation accuracy, especially in large networks with hub nodes.
Study of fixed points in large networks with random dependencies.
problem Systemic risk in large financial networks.
method Analysis of vector fixed point equations on random graphs, obtaining finite dimensional limits.
result Approximate solutions to random FP equations for large networks.
Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method of moments estimators…
Snake solves large graph optimization problems with fast proximal steps.
problem Optimization over large unstructured graphs with graph-specific regularization.
method Snake algorithm using random simple paths for proximal gradient steps.
result Convergence proven for the Snake algorithm.
A new method matches moments exactly for large graphs, improving spectral learning.
problem Lack of exact moment matching in spectral density approximations for large graphs.
method Maximum Entropy method for spectral density approximation, with a new algorithm.
result The new method outperforms existing approaches in learning graph spectra.
Crowdsourcing platforms are now extensively used for conducting subjective pairwise comparison studies. In this setting, a pairwise comparison dataset is typically gathered via random sampling, either \emph{with} or \emph{without} replacement. In this paper, we use tools from random graph theory to analyze these two ra…
Paper extends tail bounds to high-dimensional random objects on Riemannian manifolds.
problem Need for tail bounds in high-dimensional data.
method Random walks on graph approximating the manifold, ensuring spectral similarity.
result Derived tensor Chernoff bound for Riemannian manifolds.
New algorithms sample random graph homomorphisms for network analysis.
problem Sampling random graph homomorphisms from a graph into a large network.
method Proposed two MCMC algorithms with bounds on mixing times and concentration.
result Network observables are stable under renormalized cut distance.
A new method for scalable spectral clustering using random binning features.
problem Scalability issues in spectral clustering for large-scale problems.
method Random Binning features to accelerate similarity graph construction and eigendecomposition.
result Achieves similar accuracy to standard spectral clustering but with linear computational cost.
New methods learn from single graphs, improving transductive node classification.
problem Statistical foundations of transductive learning for single graphs.
method Developed new concentration-of-measure tools for large graphs.
result Achieved optimal nonparametric rate of N−1/2 for single graph learning. Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.
problem Improving graph kernel methods for better classification accuracy.
method Define and analyze walk-based node refinement methods, relate to Weisfeiler-Leman test, and introduce new walk-based kernels.
result Walk-based kernels are as expressive as Weisfeiler-Leman subtree kernel but support non-strict neighborhood comparison.
A scalable deep GMRF model for general graphs improves predictions and uncertainty estimates.
problem Handling generally structured data on graphs efficiently.
method A new multi-layer structure of Deep GMRFs designed for general graphs, enabling efficient training and close-to-exact Bayesian inference.
result Close-to-exact Bayesian inference for latent field predictions with uncertainty estimates.
Linear-time graph optimization using reinforcement learning.
problem Solving combinatorial optimization problems on real-world graphs.
method Graph neural network trained with reinforcement learning.
result Approximate solutions in linear time for various graph problems.