Maximum variance partitioning graph into disjoints cliques

Question

I am working on the following problem: Let $G = \left(V, E\right)$ an undirected graph such that every vertex $i\in V$, has a label $x_i \in \mathbb R$. For every vertex subset $S \subset V$, we define $$\text{Var}(S) = \frac1{|S|} \sum_{i \in S} \left(x_i - \frac1{|S|} \sum_{j\in S} x_j\right)^2$$ the variance of $S$. The question asks for partitioning $G$ into disjoint cliques $\left(C_k\right)_{k}$ in order to maximize the total variance $$\sum_{k}\text{Var}\left(C_k\right).$$ I think that K-means can be used here but I do not know how? Can anyone helps me to find an idea for solving this problem?