Vertex Neighborhood Maximum edges: (nv2)=12nv(nv−1)\left(\begin{array}{c} n_{v} \\ 2 \end{array}\right)=\frac{1}{2} n_{v}\left(n_{v}-1\right)(nv2)=21nv(nv−1) where nv=∣N(v)∣n_{v}=|N(v)|nv=∣N(v)∣.