  We consider the linear damped wave equation on finite metric graphs and
analyse its spectral properties with an emphasis on the asymptotic behaviour of
eigenvalues. In the case of equilateral graphs and standard coupling conditions
we show that there is only a finite number of high-frequency abscissas, whose
location is solely determined by the averages of the damping terms on each
edge. We further describe some of the possible behaviour when the edge lengths
are no longer necessarily equal but remain commensurate.
