  We formulate conditions for almost-commutative (spacetime) manifolds under
which the asymptotically expanded spectral action is renormalizable. These
conditions are of a graph-theoretical nature, involving the Krajewski diagrams
that classify such geometries. This applies in particular to the Standard Model
of particle physics, giving a graph-theoretical argument for its
renormalizability. A promising potential application is in the selection of
physical (renormalizable) field theories described by almost-commutative
geometries, thereby going beyond the Standard Model.
