  A Cayley graph over a group $G$ is said to be central if its connection set
is a normal subset of $G$. We prove that every central Cayley graph over a
simple group $G$ has at most two pairwise nonequivalent Cayley representations
over $G$ associated with the subgroups of $Sym(G)$ induced by left and right
multiplications of $G$. We also provide an algorithm which, given a central
Cayley graph $\Gamma$ over an almost simple group $G$ whose socle is of a
bounded index, finds the full set of pairwise nonequivalent Cayley
representations of $\Gamma$ over $G$ in time polynomial in size of $G$.
