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I have some relational data represented as a graph. As such some of the relational properties can be recognized. When I use the GraphLayout -> "SpectralEmbedding" option a very nice and sharply ordered graph is displayed. But what does it mean? What is GraphLayout -> "SpectralEmbedding" doing?

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    $\begingroup$ GraphLayout >> Scope >> VertexLayout >> SpectralEmbedding : Place vertices so the weighted sum of squares of mutual distances is minimized. $\endgroup$
    – kglr
    Commented Jul 6, 2016 at 19:27
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    $\begingroup$ @kglr - I read that too, but I can't figure out how to show it. If you try different embeddings in (EuclideanDistance @@@ Partition[GraphEmbedding@PathGraph[Range[20], GraphLayout -> XXX], 2, 1])^2 it doesn't show that "SpectralEmbedding" minimizes the distances. $\endgroup$
    – Jason B.
    Commented Jul 6, 2016 at 19:38
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    $\begingroup$ I assume this and its attached references are relevant. $\endgroup$
    – user484
    Commented Jul 7, 2016 at 13:33
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    $\begingroup$ Section 5 of this paper (linked in the Wiki page given by @Rahul) seems to tell me that this is the method being referred to. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Jul 7, 2016 at 16:06
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    $\begingroup$ mathematica.stackexchange.com/questions/19315/… $\endgroup$
    – Young
    Commented Jul 22, 2016 at 19:27

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