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Embedding a graph in a topological space, often Euclidean
In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation
Graph_embedding
Dimensionality reduction of graph-based semantic data objects [machine learning task]
In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine
Knowledge_graph_embedding
Graph that can be embedded in the plane
Such a drawing is called a plane graph, or a planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node
Planar_graph
Graph layout on multiple half-planes
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the
Book_embedding
Type of knowledge base
such as data reasoning, node embedding, and ontology development on knowledge bases. In contrast, virtual knowledge graphs do not store information in
Knowledge_graph
Branch of the mathematical field of graph theory
topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological
Topological_graph_theory
Planar graph drawn by relaxing springs
In graph drawing and geometric graph theory, a Tutte embedding or barycentric embedding of a simple, 3-vertex-connected, planar graph is a crossing-free
Tutte_embedding
Embedding a graph in 3D space with no cycles interlinked
Euclidean space in such a way that no two cycles of the graph are linked. A flat embedding is an embedding with the property that every cycle is the boundary
Linkless_embedding
Graph representing faces of another graph
of embedding of the graph G, so it is a property of plane graphs (graphs that are already embedded in the plane) rather than planar graphs (graphs that
Dual_graph
Representation learning technique
becomes less reliable for large embedding vectors. Latent space Feature extraction Dimensionality reduction Word embedding Neural network Reinforcement learning
Embedding_(machine_learning)
A planar graph is a graph that has such an embedding onto the Euclidean plane, and a toroidal graph is a graph that has such an embedding onto a torus
Glossary_of_graph_theory
Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
Area of discrete mathematics
imbedding) of a graph in surface and linkless embedding, graph minors, crossing number, map coloring, and voltage graph. The embedding of a graph in a surface
Graph_theory
Algorithmic problem of finding non-crossing drawings
the output of a planarity testing algorithm may be a planar graph embedding, if the graph is planar, or an obstacle to planarity such as a Kuratowski
Planarity_testing
Cubic graph with 10 vertices and 15 edges
This is the embedding given by the hemi-dodecahedron construction of the Petersen graph (shown in the figure). The projective plane embedding can also be
Petersen_graph
Mathematical puzzle of avoiding crossings
a graph embedding in the plane. The impossibility of the puzzle corresponds to the fact that K 3 , 3 {\displaystyle K_{3,3}} is not a planar graph. Multiple
Three_utilities_problem
Graph often embedded in the Klein bottle
six colors are sometimes necessary in this case. This embedding is the Petrie dual of its embedding in the projective plane shown below. It is Hamiltonian
Franklin_graph
Planar graph embedding where edges map to straight-line segments
geometric graph theory, a planar straight-line graph (PSLG), also called a straight-line plane graph or plane straight-line graph, is an embedding of a planar
Planar_straight-line_graph
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Graph with at most one crossing per edge
1-planar graph, one of the most natural generalizations of planar graphs, is drawn that way, the drawing is called a 1-plane graph or 1-planar embedding of
1-planar_graph
Mathematical result
the embedding is a random orthogonal projection. The lemma has applications in compressed sensing, manifold learning, dimensionality reduction, graph embedding
Johnson–Lindenstrauss_lemma
Visual technique in topological graph theory
from the graph, allowing holes through which the rest of the embedding can be seen. Ribbon graphs are also called fat graphs. In a ribbon graph representation
Ribbon_graph
Graph able to be embedded on a torus
the mathematical field of graph theory, a toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices and edges can be
Toroidal_graph
Undirected, connected, and acyclic graph
to an embedding of the tree in the plane, with the root at the top and the children of each vertex lower than that vertex. Given an embedding of a rooted
Tree_(graph_theory)
Graph in which every two vertices are adjacent
any three-dimensional embedding of K7 contains a Hamiltonian cycle that is embedded in space as a nontrivial knot. Complete graphs on n {\displaystyle n}
Complete_graph
Topics referred to by the same term
contained within another instance Graph embedding, in topological graph theory Embedded generation, of energy Embedding, a part of sample preparation for
Embedded
Type of monotone function
must be an order embedding. However, not every order embedding is a coretraction. As a trivial example, the unique order embedding f : ∅ → { 1 } {\displaystyle
Order_embedding
Cycles in a graph that cover each edge twice
The circular embedding conjecture or strong embedding conjecture states that every 2-vertex-connected graph has a circular embedding onto a manifold
Cycle_double_cover
Graph representing edges of another graph
a planar graph G has maximum vertex degree three, its line graph is planar, and every planar embedding of G can be extended to an embedding of L(G). However
Line_graph
Undirected cubic graph with 12 vertices and 18 edges
the Möbius strip itself) form an embedding of Tietze's graph. Tietze's graph may be formed from the Petersen graph by replacing one of its vertices with
Tietze's_graph
Embedding of the circle in three dimensional Euclidean space
the planar graphs is provided by the graphs with linkless embeddings and knotless embeddings. A linkless embedding is an embedding of the graph with the
Knot_(mathematics)
Problem in network theory
based methods. Graph embeddings also offer a convenient way to predict links. Graph embedding algorithms, such as Node2vec, learn an embedding space in which
Link_prediction
Physical simulation to visualize graphs
Koren, Yehuda (2002), "Graph drawing by high-dimensional embedding", Proceedings of the 9th International Symposium on Graph Drawing, Springer, pp. 207–219
Force-directed_graph_drawing
24-vertex symmetric bipartite cubic graph
the Nauru graph. The dual graph of this embedding is a symmetric 6-regular graph with 12 vertices and 36 edges. The other symmetric embedding of the Nauru
Nauru_graph
Projection of data onto lower-dimensional manifolds
optimizes to find an embedding that aligns the tangent spaces. Maximum Variance Unfolding, Isomap and Locally Linear Embedding share a common intuition
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Graph of numbers differing by a square
finds embeddings of the Paley graphs of order q ≡ 1 (mod 8) that are highly symmetric and self-dual, generalizing a natural embedding of the Paley graph of
Paley_graph
Non-crossing graph with vertices on outer face
outerplanarity. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is said to be k-outerplanar if
Outerplanar_graph
Visualization of node-link graphs
a graph drawing represents a graph embedding. However, nonplanar graphs frequently arise in applications, so graph drawing algorithms must generally allow
Graph_drawing
Symmetric bipartite cubic graph with 16 vertices and 24 edges
seen in the diagram above. Genus 2 embedding Genus 3 embedding The automorphism group of the Möbius–Kantor graph is a group of order 96. It acts transitively
Möbius–Kantor_graph
placement provides a simultaneous embedding. There are two restricted models: simultaneous geometric embedding, where each graph must be drawn planarly with
Simultaneous_embedding
In distributed computing and geometric graph theory, greedy embedding is a process of assigning coordinates to the nodes of a telecommunications network
Greedy_embedding
Subgraph with contracted edges
contraction of edges can increase the genus of the embedding; therefore, planar graphs and the graphs embeddable on any fixed surface form minor-closed families
Graph_minor
Fast-growing function
homeomorphically embeddable into (i.e. is a graph minor of) G j {\displaystyle G_{j}} . The Robertson–Seymour theorem proves that subcubic graphs (simple or
Friedman's_SSCG_function
Subset of artificial intelligence
Insurance Internet fraud detection Investment management Knowledge graph embedding Linguistics Machine learning control Machine perception Machine translation
Machine_learning
Graph drawing used to study Riemann surfaces
to exist, the graph must be bipartite. The faces of the embedding are required to be topological disks. The surface and the embedding may be described
Dessin_d'enfant
Matrix representation of a graph
low-dimensional embeddings that appear in many machine learning applications and determines a spectral layout in graph drawing. Graph-based signal processing
Laplacian_matrix
Graph whose embedding in a Euclidean space forms a regular tiling
In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space R n {\displaystyle \mathbb {R}
Lattice_graph
American computer scientist and educator
algorithms, with work in combinatorial optimization, graph partitioning, network flow, metric embeddings, and computational biology. Rao received the Fulkerson
Satish_B._Rao
Text-structure representation using graph models
etc. Graph-based methods for NLP and Semantic Web Representation learning methods for knowledge graphs (i.e., knowledge graph embedding) Using graphs-based
Text_graph
Set of learning techniques in machine learning
Chang, Kevin Chen-Chuan (September 2018). "A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications". IEEE Transactions on Knowledge
Feature_learning
Family of graphs with 2n nodes and n(n-1) edges
crown graph may be embedded into four-dimensional Euclidean space in such a way that all of its edges have unit length. However, this embedding may also
Crown_graph
Graph with edges of length one, able to be drawn without crossings
That is, it is a graph that has an embedding which is simultaneously a unit distance graph and a plane graph. Informally, matchstick graphs can be made by
Matchstick_graph
Theorem relating graph minors and topological embeddings
deep and fundamental connection between the theory of graph minors and topological embeddings. The theorem is stated in the seventeenth of a series of
Graph_structure_theorem
On graph drawing with integer edge lengths
planar graph have an integral Fáry embedding? More unsolved problems in mathematics In mathematics, Harborth's conjecture states that every planar graph has
Harborth's_conjecture
A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations
Periodic_graph_(geometry)
Puzzle computer game involving planar graphs
to eliminate all of the crossings and construct a straight-line embedding of the graph by moving the vertices one by one into better positions. The game
Planarity
Graph which can be made planar by removing a single node
surface embedding of G requires genus at least τ/160. However, it is NP-hard to determine the optimal genus of a surface embedding of an apex graph. By
Apex_graph
Cycle graph plus universal vertex
wheel graph with vertex set {1, 2, …, v} in which the vertex 1 is a universal vertex. Wheel graphs are planar graphs, and have a unique planar embedding. More
Wheel_graph
Largest independent set of paired elements
possible. The optimal embedding can then be obtained by pairing edges within each component and inserting each pair into an embedding, one pair at a time
Matroid_parity_problem
Polyhedral graph with 26 vertices and 39 edges
mathematical field of graph theory, the 26-fullerene graph is a polyhedral graph with V = 26 vertices and E = 39 edges. Its planar embedding has three hexagonal
26-fullerene_graph
Topics referred to by the same term
sequence Geometric genus In graph embedding, the genus of the graph is the genus of the surface in which it can be embedded In the theory of numerical
Genus_(disambiguation)
Undirected graph named after S. S. Shrikhande
vertex is surrounded by six triangles. Thus, the Shrikhande graph is a toroidal graph. The embedding forms a regular map in the torus, with 32 triangular faces
Shrikhande_graph
Representation of a graph's triconnected components
planar graph is 3-connected, it has a unique planar embedding up to the choice of which face is the outer face and of orientation of the embedding: the
SPQR_tree
Mathematical tree with cycle through leaves
embedding), and the cycle connects the leaves in their clockwise ordering in this embedding. Thus, the cycle forms the outer face of the Halin graph,
Halin_graph
Representation in natural language processing
In natural language processing, a sentence embedding (or document embedding) is a representation of a natural language text as a vector of numbers which
Sentence_embedding
have similar embedding, struc2vec captures the roles of nodes in a graph, even if structurally similar nodes are far apart in the graph. It learns low-dimensional
Struc2vec
Type of planar graph
In graph theory, a k-outerplanar graph is a planar graph that has a planar embedding in which the vertices belong to at most k {\displaystyle k} concentric
K-outerplanar_graph
Edge-face adjacencies in another graph
Since the medial graph depends on a particular embedding, the medial graph of a planar graph is not unique; the same planar graph can have non-isomorphic
Medial_graph
Format for expressing RDF statements in HTML documents
for embedding rich metadata within web documents. The Resource Description Framework (RDF) data-model mapping enables the use of RDFs for embedding RDF
RDFa
Planar, undirected graph with 2n vertices and 3n-2 edges
mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n − 2 edges. The ladder graph can be obtained as
Ladder_graph
List of unsolved computational problems
polyhedron in polynomial time? Can a simultaneous embedding with fixed edges for two given graphs be found in polynomial time? Can the square-root sum
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Type of graph in mathematics and physics
mathematics and physics, a quantum graph is a linear, network-shaped structure of vertices connected on edges (i.e., a graph) in which each edge is given a
Quantum_graph
Balanced complete multipartite graph
configuration formed by embedding a Turán graph onto the vertices of a regular simplex. An n-vertex graph G is a subgraph of a Turán graph T(n,r) if and only
Turán_graph
Database using graph structures for queries
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key
Graph_database
Subgraph induced by all nodes linked to a given node of a graph
underlying graphs of Whitney triangulations, embeddings of graphs on surfaces in such a way that the faces of the embedding are the cliques of the graph. Locally
Neighbourhood_(graph_theory)
topology and graph theory, a map is a subdivision of a surface such as the Euclidean plane into interior-disjoint regions, formed by embedding a graph onto the
Map_(graph_theory)
Graph property
Colin de Verdière's invariant is a graph parameter μ ( G ) {\displaystyle \mu (G)} for any graph G, introduced by Yves Colin de Verdière in 1990. It was
Colin de Verdière graph invariant
Colin_de_Verdière_graph_invariant
Bipartite 4-regular graph with 20 nodes and 40 edges
complete graph. Beyond the investigation of its symmetry, it has also been investigated as a counterexample for certain questions of graph embedding. Semi-symmetric
Folkman_graph
On tangency patterns of circles
itself to other objects embedded within the surface. An example comes from dessins d'enfant, a certain type of graph embedding used in algebraic geometry
Circle_packing_theorem
Symmetric tessellation of a closed surface
lines. Topological graph theory Abstract polytope Planar graph Toroidal graph Graph embedding Regular tiling Platonic solid Platonic graph Nedela (2007) Coxeter
Regular_map_(graph_theory)
On coloring the edges of graphs
polyhedral embedding is a graph embedding such that every face of the embedding is topologically a disk and such that the dual graph of the embedding is simple
Vizing's_theorem
Combinatorial theory of mechanics and discrete geometry
of the structure. A rigid graph is an embedding of a graph in a Euclidean space which is structurally rigid. That is, a graph is rigid if the structure
Structural_rigidity
Computer science algorithm
computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals
Graph_traversal
Type of topological space
regular cellulation. A loopless graph is represented by a regular 1-dimensional CW-complex. A closed 2-cell graph embedding on a surface is a regular 2-dimensional
CW_complex
Graph made from vertices and edges of a convex polyhedron
such a graph, a representation of it as a subdivision of a convex polygon into smaller convex polygons may be found using the Tutte embedding. Tait conjectured
Polyhedral_graph
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Undirected unit-distance graph requiring four colors
who constructed it (with a non-planar embedding) as a unit distance graph that requires four colors in any graph coloring. Thus, like the simpler Moser
Golomb_graph
Directed graph representing overlaps between sequences of symbols
"Laying out graphs using queues". SIAM Journal on Computing. 21 (5): 927–958. doi:10.1137/0221055. MR 1181408. Obrenić, Bojana (1993). "Embedding de Bruijn
De_Bruijn_graph
Two special graphs in graph theory
mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in the orientable
Klein_graphs
Undirected unit-distance graph requiring four colors
hull of the embedding and every bounded face is a pseudotriangle with only three convex vertices. The complement graph of the Moser graph is a triangle-free
Moser_spindle
3-regular graph with no 3-edge-coloring
In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three
Snark_(graph_theory)
Graph where all long cycles have a chord
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not
Chordal_graph
Finiteness of sets of forbidden graph minors
graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor
Robertson–Seymour_theorem
Triangle-free graph requiring four colors
graph, it can be embedded in the projective plane without crossings. This embedding has ten faces, all of which are quadrilaterals. The graph is 1-planar.
Grötzsch_graph
Type of database that uses vectors to represent other data
for each document or document section, a feature vector (known as an "embedding") is computed, typically using a deep learning network, and stored in
Vector_database
Graph drawing with vertices on a line
maximal planar graph has such an embedding if and only if it contains a Hamiltonian cycle. Therefore, a non-Hamiltonian maximal planar graph such as the
Arc_diagram
Number of planar subgraphs to cover a graph
of simultaneous embedding. If two or more planar graphs all share the same vertex set, then it is possible to embed all these graphs in the plane, with
Thickness_(graph_theory)
tree problem. Feedback vertex set Feedback arc set Graph coloring Graph homomorphism problem Graph partition into subgraphs of specific types (triangles
List_of_NP-complete_problems
Undirected graph with 14 vertices
mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and
Heawood_graph
Polish software development company
Dąbrowski, Jacek (2021-02-03). "Cleora: A Simple, Strong and Scalable Graph Embedding Scheme". arXiv:2102.02302 [cs.LG]. "Project BaseModel". Synerise AI
Synerise
GRAPH EMBEDDING
GRAPH EMBEDDING
Boy/Male
African, Arabic
Grape Vines
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Female
Thai/Siamese
Thai name A-GUN means "grape."
Boy/Male
Hindu, Indian
Efficient; Conqueror of Miseries; Bond in Affection; Capable; Mysterious; Different than Others; Smart; Most Mysterious Vastu Grah 'Rahu'; Son of Lord Buddha; Son of Goddess Durga; Truth Follower; Best of All
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Boy/Male
Arabic, Modern
Grape
Boy/Male
Muslim
Grape
Girl/Female
Indian
Grape vine
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Muslim
Grape vine
Boy/Male
Indian
Grape
Girl/Female
Indian
Grape like
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Biblical
a grape; a knot
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Muslim
Grape like
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
Girl/Female
Hindu
Grape, Belonging to kashmir
GRAPH EMBEDDING
GRAPH EMBEDDING
Boy/Male
Hindu, Indian
Guiding to the Right
Surname or Lastname
English
English : patronymic from Robin.
Girl/Female
Australian, Danish, Finnish, Indian, Swedish
Graceful; Favor
Boy/Male
Hindu
Forest (Vipin)
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Vishnu
Surname or Lastname
North German
North German : nickname for a fat man, from Middle Low German vett ‘fat’.English : nickname from Old French fait, Middle English fet ‘suitable’, ‘comely’.Norwegian : habitational name from any of several farms named with Old Norse fit ‘meadow’.
Girl/Female
Spanish Celtic
White.
Boy/Male
Indian, Sanskrit
Mentally Agile
Surname or Lastname
English and Scottish
English and Scottish : occupational name for a woodcutter or a forester (compare Woodward), or topographic name for someone who lived in the woods.English and Scottish : possibly from the Old English personal name Wudumann.
Boy/Male
Indian
Gentle
GRAPH EMBEDDING
GRAPH EMBEDDING
GRAPH EMBEDDING
GRAPH EMBEDDING
GRAPH EMBEDDING
n.
A grape of many varieties and colors.
n.
A sort of grape.
a.
Composed of, or resembling, grapes.
n.
A seed of the grape.
n.
A well-known edible berry growing in pendent clusters or bunches on the grapevine. The berries are smooth-skinned, have a juicy pulp, and are cultivated in great quantities for table use and for making wine and raisins.
n.
The plant which bears this fruit; the grapevine.
n.
The cultivation of the vine; grape growing.
n.
A variety of shaddock, called also grape fruit.
n.
See Grasshopper, and Frog hopper, Grape hopper, Leaf hopper, Tree hopper, under Frog, Grape, Leaf, and Tree.
n.
A plant of the genus Muscari; grape hyacinth.
n.
A grape, or a bunch of grapes.
a.
Resembling a grape.
n.
A grape dried in the sun; a raisin.
a.
Full of small kernels like a grape.
n.
A mangy tumor on the leg of a horse.
n.
The Hartford grape, a variety of grape first raised at Hartford, Connecticut, from the Northern fox grape. Its large dark-colored berries ripen earlier than those of most other kinds.
n.
Grapeshot.
n.
A white grape, esteemed for the table.