A centroid is a node whose removal creates components where each has at most nodes. This definition has two parts: removal (delete the node and its edges) and balance (no component too large). The centroid is the balance point of the tree. Every tree has at least one centroid. Some trees have exactly two (and they are always adjacent). Quiz: In a path of nodes (------), which node is the centroid?
Think about what happens when you remove each node.