  In many domains (e.g. Internet of Things, neuroimaging) signals are naturally
supported on graphs. These graphs usually convey information on similarity
between the values taken by the signal at the corresponding vertices. An
interest of using graphs is that it allows to define ad hoc operators to
perform signal processing. Among them, ones of paramount importance in many
tasks are translations. In this paper we are interested in defining
translations on graphs using a few simple properties. Namely we propose to
define translations as functions from vertices to adjacent ones, that preserve
neighborhood properties of the graph. We show that our definitions, contrary to
other works on the subject, match usual translations on grid graphs.
