  We construct models of exactly solvable two-particle quantum graphs with
certain non-local two-particle interactions, establishing appropriate boundary
conditions via suitable self-adjoint realisations of the two-particle
Laplacian. Showing compatibility with the Bethe ansatz method, we calculate
quantisation conditions in the form of secular equations from which the spectra
can be deduced. We compare spectral statistics of some examples to well known
results in random matrix theory, analysing the chaotic properties of their
classical counterparts.
