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Given two trees with weighted edges, what kind of similarity or distance measures are there between these two trees? Note that the number of nodes in each tree need not be the same. Are there any similarity measures that can be related to the Laplacian of these tree structures?

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My answer to this question (mathoverflow.net/questions/38305/similarity-of-weighted-graphs/…) is also applicable to your question, in case that answer is useful to you. –  Louigi Addario-Berry Sep 28 '10 at 1:55
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Susan Holmes has studied tree metrics in the case where the trees have the same number of leaves (but not necessarily vertices): www-stat.stanford.edu/~susan/papers/lap.pdf. –  R Hahn Sep 28 '10 at 2:21
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