Might mean (unverified): Graph resembling, but not Hamiltonian.
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We found one dictionary that defines the word pseudohamiltonian:

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  1. pseudohamiltonian: Wiktionary

Definitions from Wiktionary (pseudohamiltonian)

noun:  (physics) A generalization of a pseudopotential, where in addition to changing the potential the mass is varied to achieve the desired properties of the valence states.

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