title: Find parent node of a tree to create the shortest possible tree height
body: <p>I have an undirected graph represented as an adjacency matrix of Euclidean weights. I'm using this to represent the minimum spanning tree for a larger complete graph.</p>
  
  <p>What I want to find is the single node within the graph that, when used as the root node, creates the shortest possible tree height. What I've come up with is performing a depth-first traversal using every node as the root, and keeping track of the shortest height seen. Is there a faster way to accomplish this?</p>