  Symmetries are ubiquitous in real networks and often characterize network
features and functions. Here we present a generalization of network symmetry
called \emph{latent symmetry}, which is an extension of the standard notion of
symmetry. They are defined in terms of standard symmetries in a reduced version
of the network. One unique aspect of latent symmetries is that each one is
associated with a \emph{size}, which provides a way of discussing symmetries at
multiple scales in a network. We are able to demonstrate a number of examples
of networks (graphs) which contain latent symmetry, including a number of real
networks. In numerical experiments, we show that latent symmetries are found
more frequently in graphs built using preferential attachment, a standard model
of network growth, when compared to non-network like (Erd{\H o}s-R\'enyi)
graphs. Finally we prove that if vertices in a network are latently symmetric,
then they must have the same eigenvector centrality, similar to vertices which
are symmetric in the standard sense. This suggests that the latent symmetries
present in real-networks may serve the same structural and functional purpose
standard symmetries do in these networks. We conclude from these facts and
observations that \emph{latent symmetries} are present in real networks and
provide useful information about the network potentially beyond standard
symmetries as they can appear at multiple scales.

Physics and Society;Disordered Systems and Neural Networks;Social and Information Networks