@KK: DFS and BFS are O(N) and Floyd Warshall is O(N^3). 
Could you please state how you can use the traversals directly to get the 
center? (And prove your correctness too?)

The solution given by Wladimir (& expanded upon by me) is O(N) and uses 
(somewhat) the inverse of a BFS as a traversal.

--
DK

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