  We study deformations of graphical zonotopes. Deformations of the classical
permutahedron (which is the graphical zonotope of the complete graph) have been
intensively studied in recent years under the name of generalized permutahedra.
We provide an irredundant description of the deformation cone of the graphical
zonotope associated to a graph $G$, consisting of independent equations
defining its linear span (in terms of non-cliques of $G$) and of the
inequalities defining its facets (in terms of common neighbors of neighbors in
$G$). In particular, we deduce that the faces of the standard simplex
corresponding to induced cliques in $G$ form a linear basis of the deformation
cone, and that the deformation cone is simplicial if and only if $G$ is
triangle-free.
