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GraphEmbedding[g]

gives coordinates of the vertices of the graph g.

GraphEmbedding[g,"emb"]

gives coordinates of the vertices of the graph g using the embedding "emb".

GraphEmbedding[g,"emb",dim]

gives coordinates in dimension dim of the vertices of the graph g using the embedding "emb".

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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GraphEmbedding

GraphEmbedding[g]

gives coordinates of the vertices of the graph g.

GraphEmbedding[g,"emb"]

gives coordinates of the vertices of the graph g using the embedding "emb".

GraphEmbedding[g,"emb",dim]

gives coordinates in dimension dim of the vertices of the graph g using the embedding "emb".

Details

  • The settings for the embedding "emb" are the same as in GraphLayout.

Examples

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Basic Examples  (2)

Get the coordinates of the vertices of a graph:

Wolfram Language code: g = GraphData["IcosahedralGraph"]
Wolfram Language code: GraphEmbedding[g]

Obtain coordinates in two dimensions and three dimensions for spring embedding:

Wolfram Language code: g = RandomGraph[{5, 7}];
Wolfram Language code: GraphEmbedding[g, "SpringEmbedding"]
Wolfram Language code: GraphEmbedding[g, "SpringEmbedding", 3]

Scope  (23)

GraphEmbedding works with undirected graphs:

Wolfram Language code: GraphEmbedding[[image]]

Directed graphs:

Wolfram Language code: GraphEmbedding[[image]]

Multigraphs:

Wolfram Language code: GraphEmbedding[[image]]

Mixed graphs:

Wolfram Language code: GraphEmbedding[[image]]

Get the coordinates of vertices using the "BalloonEmbedding":

Wolfram Language code: GraphEmbedding[[image], "BalloonEmbedding"]

"BipartiteEmbedding":

Wolfram Language code: GraphEmbedding[[image], "BipartiteEmbedding"]

"CircularEmbedding":

Wolfram Language code: GraphEmbedding[[image], "CircularEmbedding"]

"CircularMultipartiteEmbedding":

Wolfram Language code: GraphEmbedding[[image], "CircularMultipartiteEmbedding"]

"DiscreteSpiralEmbedding":

Wolfram Language code: GraphEmbedding[[image], "DiscreteSpiralEmbedding"]

"GridEmbedding":

Wolfram Language code: GraphEmbedding[[image], "GridEmbedding"]

"HighDimensionalEmbedding":

Wolfram Language code: GraphEmbedding[[image], "HighDimensionalEmbedding"]

"LayeredEmbedding":

Wolfram Language code: GraphEmbedding[[image], "LayeredEmbedding"]

"LinearEmbedding":

Wolfram Language code: GraphEmbedding[[image], "LinearEmbedding"]

"MultipartiteEmbedding":

Wolfram Language code: GraphEmbedding[[image], "MultipartiteEmbedding"]

"PlanarEmbedding":

Wolfram Language code: GraphEmbedding[[image], "PlanarEmbedding"]

"RadialEmbedding":

Wolfram Language code: GraphEmbedding[[image], "RadialEmbedding"]

"RandomEmbedding":

Wolfram Language code: GraphEmbedding[[image], "RandomEmbedding"]

"SpectralEmbedding":

Wolfram Language code: GraphEmbedding[[image], "SpectralEmbedding"]

"SpiralEmbedding":

Wolfram Language code: GraphEmbedding[[image], "SpiralEmbedding"]

"SpringElectricalEmbedding":

Wolfram Language code: GraphEmbedding[[image], "SpringElectricalEmbedding"]

"SpringEmbedding":

Wolfram Language code: GraphEmbedding[[image], "SpringEmbedding"]

"StarEmbedding":

Wolfram Language code: GraphEmbedding[[image], "StarEmbedding"]

Get the coordinates of vertices in higher dimensions:

Wolfram Language code: GraphEmbedding[[image], "SpringEmbedding", 3]

Applications  (3)

Visualize isomorphisms between two graphs:

Wolfram Language code: {g1, g2} = {[image], [image]};
Wolfram Language code: IsomorphicGraphQ[g1, g2]
Wolfram Language code: map = FindGraphIsomorphism[g1, g2];

Reorder coordinates based on the isomorphism:

Wolfram Language code: order = VertexIndex[g2, #]& /@ (VertexList[g1] /. First[map]); vstart = GraphEmbedding[g1]; vend = GraphEmbedding[g2][[order]];

Show a transformation of one graph to another one:

Wolfram Language code: linear[x_, y_, t_] := (1 - t) x + t y;
Wolfram Language code: Table[Graph[VertexList[g1], EdgeList[g1], VertexCoordinates -> linear[vstart, vend, t], Options[g1]], {t, 0, 1, 1 / 7}]

Generate a 3D plot of a graph:

Wolfram Language code: g = RandomGraph[{10, 30}]
Wolfram Language code: coords = GraphEmbedding[g, "SpringElectricalEmbedding", 3];

Plot the graph using graphics primitives:

Wolfram Language code: Graphics3D[GraphicsComplex[coords, {Table[Sphere[VertexIndex[g, v], .1], {v, VertexList[g]}], Table[Tube[{VertexIndex[g, First[e]], VertexIndex[g, Last[e]]}, .03], {e, EdgeList[g]}]}], Boxed -> False]

Highlight cliques and subgraphs:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "FamilyGathering"}];
Wolfram Language code: clique = First[FindClique[g]]

Modify coordinates of the clique:

Wolfram Language code: coords = GraphEmbedding[g];
Wolfram Language code: Do[coords[[VertexIndex[g, i]]] += {-.1, .6}, {i, clique}];

Show the graph and the highlighted clique:

Wolfram Language code: Row[{g, HighlightGraph[g, Subgraph[g, clique], VertexCoordinates -> coords, ImagePadding -> 5]}, " ⟹ "]

Properties & Relations  (2)

Obtain vertex placement of graph layout:

Wolfram Language code: g = RandomGraph[{10, 20}]
Wolfram Language code: coords = GraphEmbedding[g]

Plot the graph using graphics primitives:

Wolfram Language code: Graphics[GraphicsComplex[coords, {Table[Point[VertexIndex[g, v]], {v, VertexList[g]}], Table[Line[{VertexIndex[g, First[e]], VertexIndex[g, Last[e]]}], {e, EdgeList[g]}]}]]

Use the option VertexCoordinates to get vertex coordinates:

Wolfram Language code: g = GraphData["IcosahedralGraph"]
Wolfram Language code: VertexCoordinates /. Options[g, VertexCoordinates]

Equivalent:

Wolfram Language code: GraphEmbedding[g]
Wolfram Research (2012), GraphEmbedding, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphEmbedding.html.

Text

Wolfram Research (2012), GraphEmbedding, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphEmbedding.html.

CMS

Wolfram Language. 2012. "GraphEmbedding." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GraphEmbedding.html.

APA

Wolfram Language. (2012). GraphEmbedding. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphEmbedding.html

BibTeX

@misc{reference.wolfram_2026_graphembedding, author="Wolfram Research", title="{GraphEmbedding}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/GraphEmbedding.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_graphembedding, organization={Wolfram Research}, title={GraphEmbedding}, year={2012}, url={https://reference.wolfram.com/language/ref/GraphEmbedding.html}, note=[Accessed: 13-June-2026]}