  Non-hermitian quantum graphs possessing real (i.e., in principle, observable)
spectra are studied via their discretization. The discretized Hamiltonians are
assigned, constructively, an elementary pseudometric and/or a more complicated
metric. Both these constructions make the Hamiltonian Hermitian, respectively,
in an auxiliary (Krein or Pontryagin) vector space or in a less friendly (but
more useful) Hilbert space of quantum mechanics.
