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"SpectralEmbedding" (Graph Layout Method)

  • Vertex layout for GraphLayout.
  • Use spectral embedding to lay out vertices of a graph.

Details & Suboptions

  • The spectral embedding is a graph-drawing technique to position vertices of a graph so they minimize the weighted sum of square distances to its adjacent vertices.
  • Vertices can be embedded in .
  • Possible settings to control the layout include:
  • "RelaxationFactor" Automaticrelaxed Laplace coefficient
    "Rotation" Automaticlayout rotation

Examples

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Basic Examples  (1)

Lay out a graph using the spectral embedding:

Wolfram Language code: Graph[{12, 13, 15, 19, 24, 26, 210, 34, 37, 311, 48, 412, 56, 57, 513, 68, 614, 78, 715, 816, 910, 911, 913, 1012, 1014, 1112, 1115, 1216, 1314, 1315, 1416, 1516}, GraphLayout -> "SpectralEmbedding"]

Options  (2)

"RelaxationFactor"  (1)

Use the option "RelaxationFactor"r to get the layout based on a relaxed Laplace matrix:

Wolfram Language code: Table[GridGraph[{10, 10}, GraphLayout -> {"SpectralEmbedding", "RelaxationFactor" -> i}], {i, 0, 1, .3}]

"Rotation"  (1)

Use "Rotation"r to rotate the layout:

Wolfram Language code: GridGraph[{10, 10}, GraphLayout -> {"SpectralEmbedding", "Rotation" -> 45 Degree}]