  We initiate the study of cluster algebras in Feynman integrals in dimensional
regularization. We provide evidence that four-point Feynman integrals with one
off-shell leg are described by a $C_{2}$ cluster algebra, and we find cluster
adjacency relations that restrict the allowed function space. By embedding
$C_{2}$ inside the $A_3$ cluster algebra, we identify these adjacencies with
the extended Steinmann relations for six-particle massless scattering. The
cluster algebra connection we find restricts the functions space for vector
boson or Higgs plus jet amplitudes, and for form factors recently considered in
$\mathcal{N}=4$ super Yang-Mills. We explain general procedures for studying
relationships between alphabets of generalized polylogarithmic functions and
cluster algebras, and use them to provide various identifications of one-loop
alphabets with cluster algebras. In particular, we show how one can obtain
one-loop alphabets for five-particle scattering from a recently discussed dual
conformal eight-particle alphabet related to the $G(4,8)$ cluster algebra.
