Generating molecular graph Laplacian based on Hückel theory
You're describing simple Hückel theory. This is usually applied to $\pi$-conjugated systems to understand the stabilization in conjugated and aromatic molecules.

There are a variety of Python packages, for example:


Felix Plasser wrote one for his blog and the current location is at his homepage
Randle Taylor has a SHMO package on GitHub, including a GUI called Orbis


I believe the version from Plasser will read in files using Open Babel's python interface, so certainly you could handle SMILES.

People would perturb the $\alpha$ (atom site energies) and $\beta$ (bond interaction) parameters in various ways. It's hard to find good tabulations of these, but the best appears to be:
"A brief review and table of semiempirical parameters used in the Hueckel molecular orbital method" J. Chem. Eng. Data 1967 122 pp. 235-246

You mention the somewhat related Extended Hückel theory (EHT). This considers both $\sigma$ and $\pi$ bonds and is thus a lot more useful, although as you mention you need coordinates to calculate overlap values, etc.