Let $\left\{\mathbf{p}_1,\dots, \mathbf{p}_k\right\}$ be a set of points in $n$-dimensional Euclidean space, and let the second moment of these points be defined as:

$ U=\sum \limits_{i=1}^{k} ||\mathbf{p}_i -\bar{\mathbf{p}}||^2, $

where $\bar{\mathbf{p}}$ is their centroid.

Let two points $i$ and $j$ be connected if $||\mathbf{p}_i - \mathbf{p}_j||\leq \lambda$.

Then, under the constraint that the points are to form a connected graph, what is the configuration that maximizes their second moment?