  We consider Laplacians on periodic both discrete and metric equilateral
graphs. Their spectrum consists of an absolutely continuous part (which is a
union of non-degenerate spectral bands) and flat bands, i.e., eigenvalues of
infinite multiplicity. We estimate effective masses associated with the ends of
each spectral band in terms of geometric parameters of graphs. Moreover, in the
case of the beginning of the spectrum we determine two-sided estimates of the
effective mass in terms of geometric parameters of graphs. The proof is based
on the Floquet theory, the factorization of fiber operators, the perturbation
theory and the relation between effective masses for Laplacians on discrete and
metric graphs, obtained in our paper.
