What would be the best book, article, or otherwise to reference for the specific construction of the classifying space for a discrete group $G$ which goes as follows?:

• Regard $G$ as a category with one object whose morphisms are the elements of $G$.
• Construct the simplicial sets $NG$ (i.e., the nerve of $G$) and $\mathcal{E}G$ (unsure if there's a standard notation; I mean that $\mathcal{E}G_n$ should be $G^{n+1}$ with face maps given by deletion and degeneracy maps given by repetition).
• Take the geometric realizations $BG$ of $NG$ and $EG$ of $\mathcal{E}G$; then $BG$ is the classifying space with universal cover $EG$.

As far as I know, this is a fairly standard construction (although perhaps not the standard one). I'm just wondering about the best place to use as a reference for it.