  Following the recent observation of wave function revivals in large Rydberg
atom quantum simulators, much effort has focused on understanding the emergence
of many-body scars in non-integrable quantum systems. Here we explore the
origin of scarred wavefunction revivals in a family of models obtained by
deforming the graph adjacency matrix of the PXP model - the effective model of
Rydberg atoms in the strong Rydberg blockade regime. We consider deformations
that either enhance the Rydberg constraint, ultimately resulting in an
effective tight-binding model of two hypercubes joined at a single vertex, or
relax the constraint until reaching the free spin-1/2 model. In the former
case, we argue that the model of two joined hypercubes captures the essential
features of many-body scarring present in the PXP model. On the other hand,
relaxing the constraint leads to a sequence of new scarred models, some with
more robust scarring signatures than the PXP model, as can be understood from
the graph-theoretic viewpoint. Our results shed light on the nature of scarring
in the PXP model by identifying its simple parent model, while also
highlighting its distinction from the free-spin precession.
