New characterization of $S_4(q)$ by its noncommuting graph

Let $G$ be a nonabelian group, and associate the noncommuting graph $\nabla(G)$ with $G$ as follows: the vertex set of $\nabla(G)$ is $G\setminus Z(G)$ with two vertices $x$ and $y$ joined by an edge whenever the commutator of $x$ and $y$ is not the identity. Let $S_4(q)$ be the projective symplectic simple group, where $q$ is a prime power. We prove that if $G$ is a group with $\nabla(G)\cong\nabla(S_4(q))$ then $G\cong S_4(q)$.