  The collective dynamics of interacting dynamical units on a network crucially
depends on the properties of the network structure. Rather than considering
large but finite graphs to capture the network, one often resorts to graph
limits and the dynamics thereon. We elucidate the symmetry properties of
dynamical systems on graph limits -- including graphons and graphops -- and
analyze how the symmetry shape the dynamics, for example through invariant
subspaces. In addition to traditional symmetries, dynamics on graph limits can
support generalized noninvertible symmetries. Moreover, as asymmetric networks
can have symmetric limits, we note that one can expect to see ghosts of
symmetries in the dynamics of large asymmetric networks.
