Suppose $\Gamma$ is a simple graph and $N_{\Gamma}(g)=\{x\in V(\Gamma)|x\sim g\}$ is the neighborhood of $g\in V(\Gamma)$. Then consider 
$$\mathbb{S}=\{y\in V(\Gamma)|N_{\Gamma}(y)=N_{\Gamma}(g)\}.$$
Is there a name in graph theory for the set $\mathbb{S}$?