  We find the set of generalized symmetries associated with the free graviton
theory in four dimensions. These are generated by gauge invariant topological
operators that violate Haag duality in ring-like regions. As expected from
general QFT grounds, we find a set of "electric" and a dual set of "magnetic'"
topological operators and compute their algebra. To do so, we describe the
theory using phase space gauge-invariant electric and magnetic dual variables
constructed out of the curvature tensor. Electric and magnetic fields satisfy a
set of constraints equivalent to the ones of a stress tensor of a $3d$ CFT. The
constraints give place to a group $\mathbb{R}^{20}$ of topological operators
that are charged under space-time symmetries. Finally, we discuss similarities
and differences between linearized gravity and tensor gauge theories that have
been introduced recently in the context of fractonic systems in condensed
matter physics.
