title: How to find the Shortest Path between all the nodes in a graph without having a pre-defined start or end points?
body: <p>What I want to get is: the path which connect all the points in my graph, but without having to tell the algorithm where to start and where to finish.</p>
  
  <p>It need to use the driving direction in google-maps api but without setting a start or end point.</p>
  
  <p>It is not the <a href="http://en.wikipedia.org/wiki/Travelling_salesman_problem" rel="nofollow noreferrer">TSP</a> problem because I don't have a "start city" and I don't have to get back to the "start city" neither.</p>
  
  <p>As expressed in this question: <a href="https://stackoverflow.com/questions/222413/find-the-shortest-path-in-a-graph-which-visits-certain-nodes">Find the shortest path in a graph which visits certain nodes</a>, 
  I could just use permutation because I have a few nodes, but the problem is that I need to analyze several groups of this few nodes So I would like the function to be the less time consuming posible.</p>
  
  <p>NOTE: Im not looking for a Minimum Spaning Tree as this one neither: <a href="https://math.stackexchange.com/questions/130863/connecting-all-points-on-a-plane-with-shortest-path-possible">https://math.stackexchange.com/questions/130863/connecting-all-points-on-a-plane-with-shortest-path-possible</a>
  I want a path which tell me you will save gas if you go first here, then overthere, then overthere, and finally there.</p>
  
  <p><strong>Question:</strong> is there any library which can help me with that? Or is it a know problem that has already an exact answer? How could I solve it?</p>