LeetCode 310 Minimum Height Trees - Strategy

You could find the Diameter and pick the middle, but there is another intuitive approach: Topological Peeling. Start from the leaves (nodes with degree $1$) and peel them off layer by layer. After each layer is removed, new leaves appear. Keep peeling until only $1$ or $2$ nodes remain. These are the centers. Why?

Because the centers are the nodes furthest from all leaves. Peeling removes the outer layers, leaving the core.