I was just thinking recently about if there are any possible meaningful connections between tools such as persistent homology used for things like topological data analysis and tools used in spectral graph theory (I don’t have really any experience with spectral graph theory besides the basic notions and my topology background is limited as well).

Can eigenvalues of some matrix associated with some (possibly random) data/clusters give insight to any topological features of this data? Or can performing things like persistent homology on data to reveal certain features of this data give rise to questions about eigenvalues of some associated matrix?

  • $\begingroup$ arxiv.org/pdf/1707.06683.pdf ...I highly suspect it can..if you read 3.2 in this paper. $\endgroup$ – Shogun Aug 4 '18 at 1:45
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    $\begingroup$ I will check that out! I completely forgot I had asked this question... I wish I worded it a bit better but I was thinking about this stuff with very minimal exposure to both fields. I have more knowledge now, but have not thought about this in a long time. Would love to see if anybody has anything to contribute. $\endgroup$ – Corey Aug 4 '18 at 10:04
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    $\begingroup$ This paper was just published and may be of use to anyone interested arxiv.org/pdf/1808.01513.pdf $\endgroup$ – Corey Aug 7 '18 at 21:53

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