  We investigate the viscoelastic relaxation to equilibrium of a disordered
planar epithelium described using the cell vertex model. In its standard form,
the model is formulated as coupled evolution equations for the locations of
vertices of confluent polygonal cells. Exploiting the model's gradient-flow
structure, we use singular-value decomposition to project modes of deformation
of vertices onto modes of deformation of cells. We show how eigenmodes of
discrete Laplacian operators (specified by constitutive assumptions related to
dissipation and mechanical energy) provide a spatial basis for evolving fields,
and demonstrate how the operators can incorporate approximations of
conventional spatial derivatives. We relate the spectrum of relaxation times to
the eigenvalues of the Laplacians, modified by corrections that account for the
fact that the cell network (and therefore the Laplacians) evolve during
relaxation to an equilibrium prestressed state, providing the monolayer with
geometric stiffness. While dilational modes of the Laplacians capture rapid
relaxation in some circumstances, showing diffusive dynamics, geometric
stiffness is typically a dominant source of monolayer rigidity, as we
illustrate for monolayers exposed to unsteady stretching deformations.
