  Symmetric special multiserial algebras are algebras that correspond to
decorated hypergraphs with orientation, called Brauer configurations. In this
paper, we use the combinatorics of Brauer configurations to understand the
module category of symmetric special multiserial algebras via their
Auslander-Reiten quiver. In particular, we provide methods for determining the
existence and ranks of tubes in the stable Auslander-Reiten quiver of symmetric
special multiserial algebras using only the information from the underlying
Brauer configuration. Firstly, we define a combinatorial walk around the Brauer
configuration, called a Green `hyperwalk', which generalises the existing
notion of a Green walk around a Brauer graph. Periodic Green hyperwalks are
then shown to correspond to periodic projective resolutions of certain classes
of string modules over the corresponding symmetric special multiserial algebra.
Periodic Green hyperwalks thus determine certain classes of tubes in the stable
Auslander-Reiten quiver, with the ranks of the tubes determined by the periods
of the walks. Finally, we provide a description of additional rank two tubes in
symmetric special multiserial algebras that do not arise from Green hyperwalks,
but which nevertheless contain string modules at the mouth. This includes an
explicit description of the space of extensions between string modules at the
mouth of tubes of rank two.
