Solves Skopenkov's problem on graph embedding criteria.
problem Criteria for toroidal embedding of one-vertex ribbon graphs.
method Analyzes one-vertex ribbon graphs with additional disc structure.
result Provides solutions to Skopenkov's problem.
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168,695 papers · 148 categories
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48 results for “vertex graphs”
New invariants distinguish spatial graphs not previously possible.
problem Distinguishing spatial graphs using Dehn colorings.
method Developed vertex-weight invariants based on Dehn colorings.
result Found spatial graphs distinguishable by vertex-weight invariants.
Enhances graph classification with multiple graphs.
problem Improving graph classification accuracy with multiple graphs.
method Graph fusion embedding using encoder embedding.
result The method consistently improves classification accuracy for large vertex sets.
While many multiple graph inference methodologies operate under the implicit assumption that an explicit vertex correspondence is known across the vertex sets of the graphs, in practice these correspondences may only be partially or errorfully known. Herein, we provide an information theoretic foundation for understand…
In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex grid structures, and define a new vertex convolution operation by adopting a set of…
Efficient method for vertex embedding and community detection.
problem Vertex embedding and community detection.
method Normalized one-hot graph encoder and rank-based cluster size measure.
result Excellent numerical performance of graph encoder ensemble algorithm.
The study proves unique harmonic functions and combinatorial properties of vertex-transitive graphs.
problem Proving combinatorial properties of vertex-transitive graphs.
method Using harmonic functions and quasi-isometry to , proving uniqueness and combinatorial results.
result Connective constant of non-degenerate vertex-transitive graphs is at least the golden mean.
Proves minimal crossing diagrams for specific spatial graphs.
problem Proving minimal crossing diagrams for spatial graphs.
method Analyzing adequate diagrams and replacing vertices and edges.
result All 1-vertex spatial graphs with adequate diagrams have minimal crossing number.
Graph Lie algebras have infinite prolongation if they have a vertex of degree one.
problem Determining when the prolongation of a graph Lie algebra is infinite-dimensional.
method Analyzing labeled direct graphs and their associated Lie algebras.
result Graph Lie algebras are infinite-dimensional if and only if they have a vertex of degree one.
In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random -regular graphs. Moreover we show that …
The paper explores how to find relevant vertices in one graph using another graph's attributes and structure.
problem Finding relevant vertices in one graph using another graph's attributes and structure.
method Theoretical and practical exploration of vertex nomination schemes that leverage both content (edge and vertex attributes) and context (network topology).
result Necessary and sufficient conditions for schemes that use both content and context to outperform those using only one.
Proves a generalized Whitehead cut vertex lemma for tree groups.
problem Extending Whitehead's cut vertex lemma to tree group conjugacy classes.
method Proves a version of Whitehead's lemma for tree groups.
result Establishes a cut vertex in star graphs for tree group conjugacy classes.
Algorithm learns graph ARMA processes for missing signal estimation.
problem Missing signal estimation in time-varying graph signals.
method Learning joint time-vertex power spectral density through convex relaxations.
result High accuracy in time-vertex signal estimation.
Convolutional layers in graph neural networks are a fundamental type of layer which output a representation or embedding of each graph vertex. The representation typically encodes information about the vertex in question and its neighbourhood. If one wishes to perform a graph centric task, such as graph classification,…
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the 2-component constituent algebraically split links and show examples…
The paper introduces a method for detecting principal communities and embedding vertices.
problem Detecting and embedding vertices in graphs with community structure.
method Principal graph encoder embedding method that detects principal communities and produces vertex embeddings.
result The method successfully detects principal communities and produces accurate vertex embeddings.
The paper classifies palettes of Dehn colorings for spatial graphs.
problem Classifying spatial graph diagrams using Dehn colorings.
method Examining vertex conditions and palettes for spatial graphs.
result Spatial graphs can be distinguished by the number of Dehn colorings with specific palettes.
Gaussian processes classify graphs using vertex and edge features.
problem Graph classification in machine learning.
method Transform graph features into spectral Euclidean features, apply Hodge decomposition.
result Gaussian processes can classify graphs using vertex and edge features.
Lower bound on minimum vertex degree for non-negative Lin-Lu-Yau curvature on graphs.
problem Determining the minimum vertex degree for non-negative Lin-Lu-Yau curvature.
method Investigation of Ollivier-Ricci curvature and Lin-Lu-Yau modification on locally finite graphs.
result Lower bound on minimum vertex degree ensuring non-negative Lin-Lu-Yau curvature.
The paper introduces a quantum state system to count perfect matchings in graphs.
problem Counting perfect matchings in graphs using quantum state systems.
method Topological quantum field theory (TQFT) and spectral sequences.
result The filtered -color vertex homology for is generated by perfect matchings.
Improved graph embedding through refined linear transformation and community recovery.
problem Identifying meaningful latent communities in graph data.
method Refined graph encoder embedding via linear transformation, self-training, and latent community recovery.
result Improved vertex embedding and better decision boundaries for vertex 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.
Proposes methods to recover labels from shuffled networks using graph averages.
problem Recovering labels from a shuffled network using graph averages.
method Cluster networks into classes, then match the new graph to cluster-averages, minimizing the graph matching objective function.
result Higher fidelity matching performance when clustering networks into different classes.
The Kauffman-Vogel polynomials are three variable polynomial invariants of -valent rigid vertex graphs. A one-variable specialization of the Kauffman-Vogel polynomials for unoriented -valent rigid vertex graphs was given by using the Kauffman bracket and the Jones-Wenzl idempotent colored with . Bataineh, Elha…
Graph cross network improves graph classification accuracy.
problem Improving graph classification accuracy.
method Graph cross network (GXN) with vertex infomax pooling (VIPool) and feature-crossing layer.
result Improves graph classification accuracy by 2.12% and 1.15%.
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. Fleming and the author introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the constituent 2-component algebraically split li…
The paper studies graph products of groups and recovers graph and vertex groups under certain conditions.
problem Recovering graph and vertex groups from graph products of groups.
method Using non-generic almost positive sentences, the authors show that under specific conditions, the underlying graph and vertex groups can be recovered.
result The core of the defining graph determines an invariant of the elementary theory of a right-angled Artin group.
Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.
New methods cluster and test graphs without vertex correspondence.
problem Clustering and testing of networks without vertex correspondence.
method Inspired by graphon estimation, propose a novel graph distance and clustering algorithms.
result Prove statistical consistency of clustering algorithms under Lipschitz assumptions on graph degrees.
Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list. Previous work has yielded several approaches to this problem, with theoretical re…
Two spectral algorithms for community detection in graphs with covariates are compared.
problem Detecting community structure in graphs with covariates.
method Two model-based spectral algorithms are presented and compared.
result The second algorithm often better estimates block assignments by accounting for vertex covariates.
Optimal Reeb graphs identified for polygon decomposition.
problem Investigating the topological structure of planar polygon decomposition.
method Using oriented Reeb graphs with a marked vertex for height functions.
result Described all possible optimal Reeb graphs for specific polygon configurations.
Robust Vertex Classificationstat.ML
For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, w…
It is well-known that the Pachner graph of -vertex triangulated -spheres is connected, i.e., each pair of -vertex triangulated -spheres can be turned into each other by a sequence of edge flips for each . In this article, we study various induced subgraphs of this graph. In particular, we prove tha…
An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised representation learning have been demonstrated to give the state-of-the-art perfor…
On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groupsmath.CO
We prove that the Cayley graph and the coset geometry of the von Dyck group are linked by a vertex-to-edge duality.
Connected components of Morse boundaries are studied in graph of groups.
problem Understanding the structure of Morse boundaries in graph of groups.
method Analyzes connected components of Morse boundaries, considering edge and vertex groups properties.
result Connected components of Morse boundaries are derived from vertex groups under certain conditions.
Paper studies vertex correspondence recovery in correlated graphs with node features.
problem Recovering hidden vertex correspondence between two correlated graphs with observed edge weights and node features.
method Introduced featured correlated Gaussian Wigner model and proposed QPAlign algorithm for quadratic programming relaxation.
result Characterized optimal information-theoretic thresholds for exact and partial recovery of latent mapping.
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.
Seeded Graph Matchingstat.ML
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first given a partial alignment that we are tasked with completing. In this paper, we m…
An Inaccessible Graphmath.GR
An inaccessible, vertex transitive, locally finite graph is described. This graph is not quasi-isometric to a Cayley graph.
New formulas for spatial 2-bouquet graphs discovered.
problem Finding formulas for Vassiliev invariants of spatial 2-bouquet graphs.
method Introducing new Gauss diagram formulas for flat vertex isotopy classes of spatial 2-bouquet graphs.
result First simple example of a Gauss diagram formula for spatial 2-bouquet graphs.
New bounds on maximal linkless graphs with improved edge-to-vertex ratios.
problem Finding maximal linklessly embeddable graphs with improved edge-to-vertex ratios.
method Constructing families of graphs and proving necessary and sufficient conditions for clique sums.
result Improved edge-to-vertex ratios for maximal linklessly embeddable graphs.
Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query…
DeepMap learns deep graph representations via CNNs, improving graph classification performance.
problem Quantifying graph similarities for tasks like classification.
method Proposes DeepMap framework extending CNNs to arbitrary graphs, learning dense low-dimensional vectors.
result DeepMap achieves state-of-the-art performance on graph classification benchmarks.
Motivated by his studies in knot theory V. Vassiliev introduced -graphs as regular 4-valent graph with a structure of pairs of opposite edges at each vertex. He conjectured the conditions under which -graph can be embedded into a plane respecting the the -structure at every vertex. The conjecture was proved by…
Approximates cycles in planar and bounded-genus graphs.
problem Finding many disjoint cycles in planar and bounded-genus graphs.
method Constant-factor approximation algorithms for vertex-disjoint and edge-disjoint cycles.
result First algorithms for vertex-disjoint paths in fully planar and bounded-genus instances.
We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary graphs of groups, we show that if their fundamental group is not one-ended, then we can blow up vertex groups to graphs of groups with simp…