In graph drawing, suppose we have G=(V,E), A graph drawing $ρ:V\rightarrow R^n$
We can formalize this by defining the energy of a drawing $R$ by $$ \mathcal{E}(R)=\sum_{\left\{v_{i}, v_{j}\right\} \in E}\left\|\rho\left(v_{i}\right)-\rho\left(v_{j}\right)\right\|^{2}, $$
Proposition 2.1. Let $G=(V, W)$ be a weighted graph, with $|V|=m$ and $W$ an $m \times m$ symmetric matrix, and let $R$ be the matrix of a graph drawing $\rho$ of $G$ in $\mathbb{R}^{n}$ (am $m \times n$ matrix). If $L=D-W$ is the unnormalized Laplacian matrix associated with $W$, then $$ \mathcal{E}(R)=\operatorname{tr}\left(R^{\top} L R\right) . $$
I don't know how do I prove this Proposition .....