User:MWinter4/Graph embedding
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In graph theory a graph embedding (also graph realization, representation or drawing) is a way to reconsider an abstract graph as a geometric object. This happens, as the name suggests, by embedding the graph in some Euclidean space, surface or more general manifold, where the interpretation of "embedding" in the sense of injective is not always followed strictly. The two most important uses of the term graph embedding are
- straight-line embeddings, which only describe the placement of vertices and consideres edges as straight lines between them. Examples are spectral embeddings, nullspace embeddings, Colin de Verdière embeddings, planar straight-line embeddings or polytope skeleta. Especially for embeddings that result from computational processes (such as spectral embeddings), injectivity is not a strict requirement (and is usually hard to enforce for the edges).
- tological embeddings, where not only vertices are placed, but each edge is described by a continuous curve between its end vertices. These most often occur in topological graph theory and graph drawing.
Spectral graph embedding
Topological graph embedding
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