"combinatorial embedding". An embedded graph also defines natural cyclic orders of edges which constitutes the boundaries of the faces of the embedding. However...

In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine...

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...

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...

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...

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...

such as data reasoning, node embedding, and ontology development on knowledge bases. In contrast, virtual knowledge graphs do not store information in...

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...

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...

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...

geometric graph theory, a planar straight-line graph (or straight-line plane graph, or plane straight-line graph), in short PSLG, is an embedding of a planar...

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...

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...

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...

resulting embeddings vary by type, including word embeddings for text (e.g., Word2Vec), image embeddings for visual data, and knowledge graph embeddings for...

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...

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...

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...

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...

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...

another instance Graph embedding Embedded generation, a distributed generation of energy, also known as decentralized generation Self-embedding, in psychology...

a graph drawing represents a graph embedding. However, nonplanar graphs frequently arise in applications, so graph drawing algorithms must generally allow...

The circular embedding conjecture or strong embedding conjecture states that every 2-vertex-connected graph has a circular embedding onto a manifold...

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...

based methods. Graph embeddings also offer a convenient way to predict links. Graph embedding algorithms, such as Node2vec, learn an embedding space in which...

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...

Koren, Yehuda (2002), "Graph drawing by high-dimensional embedding", Proceedings of the 9th International Symposium on Graph Drawing, Springer, pp. 207–219...

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}...

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...

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...