NeuroMatch efficiently matches subgraphs in large graphs using neural networks.
problem Determining the presence and location of a query graph in a large target graph.
method NeuroMatch decomposes graphs into subgraphs, embeds them using graph neural networks, and matches them directly in the embedding space.
result NeuroMatch is 100x faster and 18% more accurate than existing methods.
Efficiently matches subgraphs in noisy data without node labels.
problem Subgraph isomorphism in noisy, real-valued graphs.
method Two-step approach: extract topology, then expand matches.
result Realistically sub-linear computational efficiency, robustness to noise.
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by …
GraphDETR detects subgraphs in large graphs using deep learning.
problem Detecting subgraphs in large graphs efficiently and accurately.
method Formulates subgraph detection as a set prediction problem using GraphDETR, a deep learning framework.
result GraphDETR can detect diverse patterns in large graphs, achieving strong performance on molecular functional group detection.
GraphQ system uses GNNs to search for subgraph patterns in graphs.
problem Efficiently identifying and matching subgraph patterns in graph data.
method Graph neural networks (GNNs) for encoding graph data and NeuroAlign for node alignment.
result NeuroAlign improves node-alignment accuracy by 19-29% compared to baseline GNNs.
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.
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank \cite{Frank1978} of estimating the number of connected components in a large graph based …
GLSearch uses GNN to learn efficient search strategies for finding large common subgraphs.
problem Finding the Maximum Common Subgraph (MCS) between two graphs is NP-hard and hard to solve efficiently.
method GLSearch combines GNN and DQN to learn optimal node pairs for expansion in a branch and bound algorithm.
result GLSearch finds significantly larger common subgraphs than heuristic search methods given the same computation budget.
Applied researchers often construct a network from a random sample of nodes in order to infer properties of the parent network. Two of the most widely used sampling schemes are subgraph sampling, where we sample each vertex independently with probability p and observe the subgraph induced by the sampled vertices, and…
Robust GW distance improves graph data alignment.
problem Outliers in GW distance lead to inaccurate comparisons.
method Optimistically perturbed marginal constraints within a Kullback-Leibler divergence-based ambiguity set.
result RGW reduces inaccuracies in graph data alignment.
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost function is a general nonlinear function and, in particular, the sparsity constrain…
This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.
problem Recovering hidden vertex correspondences in partially correlated graphs.
method Proposed partially correlated Erdős-Rényi graphs model; information-theoretic thresholds; correlated functional digraphs.
result Optimal rates for partial and exact recovery of vertex correspondences.
SubGNN tackles subgraph prediction challenges in graphs.
problem Subgraphs in graphs are challenging to predict due to their internal topology and external connectivity.
method SubGNN introduces a novel subgraph routing mechanism to learn disentangled subgraph representations.
result SubGNN achieves considerable performance gains on subgraph classification tasks, outperforming strong baseline methods.
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph matching methods can be applied directly to recover the missing correspondences,…
GraphMoE generates random graphs using neural networks and graphlets.
problem Learning generative models for random graphs.
method GraphMoE uses a neural network trained with graphlets and subgraph counts to match the distribution of random graphs.
result GraphMoE can generate graphs that mimic various real-world datasets and fool graph classifiers.
A biclustering algorithm finds dense disjoint subgraphs in weighted bipartite graphs.
problem Finding dense disjoint bicliques in a weighted bipartite graph.
method Semidefinite programming-based branch-and-cut algorithm with upper and lower bounds.
result The algorithm can solve much larger instances than general-purpose solvers.
The paper introduces subgraph nomination for finding similar subgraphs in networks.
problem Finding similar subgraphs in networks using example subgraphs.
method Formalizes subgraph nomination framework with user-supervised retrieval.
result User-supervised retrieval improves performance in subgraph nomination.
The paper develops bounds for predictive values in binary classification.
problem Lack of confidence intervals for positive and negative predictive values.
method Bi-criterion framework and distribution-free large deviation and uniform convergence bounds.
result New bounds for predictive values without relying on concentration inequalities.
The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding…
Unified framework for subgraph-enhanced GNNs, improving prediction accuracy and reducing computation time.
problem Limited understanding of subgraph-enhanced GNNs and their relation to the Weisfeiler-Leman hierarchy.
method Theoretical framework, theoretical expressivity results, and data-driven subgraph sampling methods.
result Data-driven subgraph-enhanced GNNs outperform non-data-driven methods in predictive performance.
Study area-minimizing subgraphs in integer lattices.
problem Finding the most efficient subgraphs in integer lattices.
method Formulated functions of bounded variations, classified subgraphs in 2D, proved properties in higher dimensions.
result Classified area-minimizing subgraphs in 2D integer lattice up to isomorphisms.
GNNS uses graph neural networks to efficiently estimate subgraph frequency distributions.
problem Efficiently calculating subgraph frequency distributions in large networks.
method Graph Neural Networks (GNNS) for sampling and estimating subgraph frequencies.
result GNNS achieves comparable accuracy with a significant speedup of three orders of magnitude.
Proposes GIB for recognizing informative subgraphs in graphs.
problem Recognizing a subgraph that is maximally informative yet compressive.
method Graph Information Bottleneck (GIB) framework, mutual information estimator, bi-level optimization, connectivity loss.
result IB-subgraph improves graph classification, interpretation, and denoising.
We consider the densest k-subgraph problem, which seeks to identify the k-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We propose a new convex relaxation for the densest k-subgraph problem, based on a nucle…
RevTrack identifies suspicious subgraphs on blockchain for AML.
problem Detecting money laundering in cryptocurrency transactions.
method Graph-based machine learning, tracking initial senders and final receivers.
result RevClassify outperforms state-of-the-art subgraph classification techniques in cost and accuracy.
Faster algorithm for generalized mean densest subgraph problem.
problem Finding subgraphs with highest average p-th-power degree. method GENPEEL++ algorithm, which yields (2(p+1))1/p-approximation for p∈[1,+∞) with time complexity O(m(logn)). result GENPEEL++ algorithm provides faster and more efficient solution for generalized mean densest subgraph problem.
Let Γ be a finite graph and let Γe be its extension graph. We inductively define a sequence {Γi} of finite induced subgraphs of Γe through successive applications of an operation called "doubling along a star". Then we show that every finite induced subgraph of Γe is iso…
Classification and regression in which the inputs are graphs of arbitrary size and shape have been paid attention in various fields such as computational chemistry and bioinformatics. Subgraph indicators are often used as the most fundamental features, but the number of possible subgraph patterns are intractably large …
Mining discriminative subgraph patterns from graph data has attracted great interest in recent years. It has a wide variety of applications in disease diagnosis, neuroimaging, etc. Most research on subgraph mining focuses on the graph representation alone. However, in many real-world applications, the side information …
Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.
problem Estimating eigenvalues of poly-Laplace operator on subgraphs of lattice graphs.
method Introduced discrete poly-Laplace operator, derived upper and lower bounds for eigenvalues.
result Poly-Laplace eigenvalues are at least squares of lower-order poly-Laplace eigenvalues.
ESAN improves graph neural networks by processing subgraphs.
problem Limitations of MPNNs in graph isomorphism.
method ESAN represents graphs as sets of subgraphs and processes them with equivariant architectures.
result ESAN increases the expressive power of GNNs and more expressive architectures.
Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interestingness of discriminative subgraph features are defined on certain graphs, where the structure of graph objec…
Sparse neural networks can match dense models on Lipschitz functions.
problem Sparse networks are more efficient but lack theoretical guarantees.
method Formal model of sparse networks, LSH-based routing function, Lipschitz function approximation.
result Sparse networks can approximate dense networks on Lipschitz functions.
In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it …
We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, …
Upper bounds for Steklov eigenvalues in subgraphs of polynomial growth Cayley graphs.
problem Finding upper bounds for Steklov eigenvalues in subgraphs of polynomial growth Cayley graphs.
method Discretizing a bounded domain and using comparison theorems.
result The $k^{\mbox{th}}$ eigenvalue tends to 0 proportionally to 1/∣B∣d−11. GMT improves interpretability of XGNNs by approximating SubMT.
problem Limited understanding of existing interpretable subgraph learning methods.
method Formulated subgraph multilinear extension (SubMT) and designed GMT architecture.
result GMT outperforms state-of-the-art in both interpretability and generalizability.
Introduces a new manifold from a graph subgraph.
problem None explicitly stated in the abstract.
method Defined geometrically from a combinatorial subgraph of the Hoffman-Singleton graph.
result Geometric properties of the new manifold presented.
SELO model predicts link signs better than SDGNN using subgraph encoding and linear optimization.
problem Inferring the sign of links in signed networks with limited sign data.
method Subgraph Encoding via Linear Optimization (SELO) approach to learn edge embeddings.
result SELO model outperforms state-of-the-art methods on multiple real-world signed networks.
XploVAE improves recommendation by balancing known and novel items.
problem Balancing known and novel items for better recommendations.
method Constructs user-specific subgraphs for exploitation and exploration, learns personalized item embeddings.
result Demonstrates effectiveness on various real-world datasets.
Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact an…
Neural network for subgraph similarity computation with pruning.
problem Computing subgraph similarity between a target and query graph.
method Convert pruning to node relabeling, relax to differentiable problem, design neural network for SED computation.
result Establishes new state-of-the-art results across multiple benchmark datasets.
Metric graphs have subgraphs with entropy at least λ.
problem Finding subgraphs with high entropy in metric graphs.
method Proving existence of subgraphs with entropy at least λ for graphs of rank r with entropy 1.
result Metric graphs have subgraphs with entropy at least λ.
Efficient algorithm for graph matching in correlated stochastic block models.
problem Graph matching in correlated stochastic block models with balanced communities.
method Extends previous work on centered subgraph counts to handle estimation errors and edge correlation.
result First efficient algorithm for graph matching in the logarithmic average degree regime, matching all but a vanishing fraction of vertices with high probability.
The study extends Tutte's conflict graph concept to nonplanar graphs.
problem Understanding the structure of nonplanar graphs through conflict graphs.
method Defining a signed conflict graph for maximally planar subgraphs and analyzing their balance.
result For graphs with a flat embedding, every maximal planar subgraph has unbalanced conflict graphs if and only if the graph is intrinsically linked.
Finite subgraphs in flip graphs ensure unique surface embeddings.
problem Ensuring unique embeddings of surfaces based on flip graphs.
method Analyzing finite subgraphs within flip graphs of surfaces.
result Injective homomorphisms are uniquely extendable and induced by embeddings.
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
Cohomology defines hyperbolic spaces and their subgraphs.
problem Characterizing hyperbolic spaces and their subgraphs.
method Complete cohomological characterization using ℓ∞-cohomology. result Cohomology vanishing characterizes hyperbolicity and acylindrical hyperbolicity.