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In quantum graph theory, what are the properties of a given graph to own complex conjugated complex eigenvalues, either finite or infinite? Spectral graph theory is as far as I know a not completely developed branch for spectra of "infinite graphs". Some useful reference would be welcome (for spectral graph theory of infinite graphs).

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Infinite graphs is delicate topic in Spectral Graph theory because there are many technical considerations for the theory to even make sense.

In the mathematical realm theories for infinite graphs, more accurately "graph limits" include:

Lovasz's work on "Graphons" in the dense case, ( and Chungs work on "Graphlets" in the sparse case. (

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