Let be a finite graph and let be its extension graph. We inductively define a sequence of finite induced subgraphs of through successive applications of an operation called "doubling along a star". Then we show that every finite induced subgraph of is iso…
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48 results for “finite subgraphs”
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.
Let be an orientable surface of genus with punctures. We identify a finite rigid subgraph of the pants graph , that is, a subgraph with the property that any simplicial embedding of into any pants graph is induced by an embedding $S_{g…
Estimates eigenvalues and spectrum for graph substructures using isocapacitary constants.
problem Estimating eigenvalues and spectrum for graph substructures.
method Introducing Cheeger type constants via isocapacitary constants to estimate eigenvalues and spectrum.
result Estimates for first Dirichlet, Neumann, and Steklov eigenvalues, as well as the bottom of the spectrum of the Laplace operator and Dirichlet-to-Neumann operator.
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.
The study constructs links from polytope subgraphs and proves their hyperbolic properties.
problem Proving hyperbolic structures for links from polytope subgraphs.
method Construction of 3-manifolds from polytope subgraphs and analysis of their topology.
result Hyperbolic links are parametrized by specific subgraphs in hyperbolic polytopes.
We prove a strong form of finite rigidity for pants graphs of spheres. Specifically, for any , we construct a finite subgraph of the pants graph of the n-punctured sphere with the following property. Any simplicial embedding of into any pants graph of a punctured …
VISTA learns causal structures by integrating local subgraphs, improving accuracy and efficiency.
problem Efficiently learning causal structures from high-dimensional observational data.
method VISTA decomposes the global causal structure learning problem into local subgraphs based on Markov Blankets, integrating them via a weighted voting mechanism.
result VISTA achieves notable improvements in accuracy and efficiency over existing methods.
The fine curve graph is hyperbolic and contains all countable graphs as induced subgraphs.
problem Characterizing the structure and properties of fine curve graphs.
method Analyzing the hyperbolicity and induced subgraph properties of fine curve graphs and their direct limits.
result The finitary curve graph has diameter 2, contains every countable graph as an induced subgraph, and has the homeomorphism group of the surface as its automorphism group.
New findings on hyperbolicity of fine curve graphs and their subgraphs.
problem Investigating hyperbolicity of fine curve graphs and their subgraphs.
method Analyzing large subgraphs of fine curve graphs and computing distances in specific cases.
result Large subgraphs of fine curve graphs contain flats of every finite dimension, indicating they are not hyperbolic.
We show that for a sufficiently simple surface , a right-angled Artin group embeds into $\Mod(S)$ if and only if embeds into the curve graph $\mC(S)$ as an induced subgraph. When is sufficiently complicated, there exists an embedding $A(Γ)\to\Mod(S)$ for some not contained in $\mC(S)$.
Embedding right-angled Artin groups in mapping class groups of nonorientable surfaces.
problem Embedding right-angled Artin groups in mapping class groups for nonorientable surfaces.
method Proving embedding for finite full subgraphs and some non-full subgraphs of curve graphs.
result Existence of non-full subgraphs that can be embedded in mapping class groups.
Our main theorem asserts that every Farey graph embedded in the 1-skeleton of the pants complex of any finite type surface is totally geodesic.
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.
Koberda proved that if a graph is a full subgraph of a curve graph of an orientable surface , then the right-angled Artin group on is a subgroup of the mapping class group of . On the other hand, for a sufficiently complicated surface , Kim-Koberda gave a graph $Γ…
Graph neural networks struggle with counting certain substructures in graphs.
problem Detecting and counting specific substructures in graphs.
method Study of graph neural networks' ability to count attributed graph substructures.
result Graph neural networks like MPNNs, 2-WL, and 2-IGNs have limitations in counting certain substructures.
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.
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.
Graphs with specific spanning trees yield RAAGs, with applications to BBGs.
problem Recognizing when Bestvina-Brady groups are right-angled Artin groups.
method Using Bieri-Neumann-Strebel invariants and spanning trees of graphs.
result Characterization of BBGs that are RAAGs.
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.
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 …
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.
In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph $\gam$, we produce a new graph through a purely combinatorial procedure, and call it the extension graph $\gam^e$ of $\gam$. We produce a second graph $\gam^e_k$, the clique graph of $\gam^e$, by adding …
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 say a graph has property when it is an induced subgraph of the curve graph of a surface of genus with punctures. Two well-known graph invariants, the chromatic and clique numbers, can provide obstructions to . We introduce a new invariant of a graph, the 'nested complex…
We consider the densest -subgraph problem, which seeks to identify the -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 -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 -th-power degree.
method GENPEEL++ algorithm, which yields -approximation for with time complexity .
result GENPEEL++ algorithm provides faster and more efficient solution for generalized mean densest subgraph problem.
Paper tackles NP-complete subgraph isomorphism counting problem.
problem Counting subgraph isomorphisms in large graphs.
method Learning framework that augments representation learning architectures and iteratively attends pattern and target graphs.
result Scalable learning approach counts subgraph isomorphisms in linear time.
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 …
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.
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…
We show that the asymptotic dimension of a hyperbolic relatively hyperbolic graph is finite provided that this holds true uniformly for the peripheral subgraphs and for the electrifiation. We use this to show that the asymptotic dimension of the disk graph of a handlebody of genus at least two is at most quadratic in t…
A new estimator combines bootstrapping and rollout methods in RL.
problem Combining strengths of bootstrapping and rollout methods in RL.
method Subgraph Bellman operators and fixed point solving.
result Upper bound on error approaches optimal TD variance with additional term.
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 proportionally to .
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.
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.
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.
Subgraph Entropymath.GT
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.
Estimates social network structure from random walk subgraphs.
problem Recovering population structure from random walk subgraphs in stochastic block models.
method Maximum likelihood estimation, SAEM algorithm, de-biasing techniques.
result New de-biased estimator provides more accurate recovery of network structure.
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.