title: What is the best way (algorithm) to find most weighted path in a weighted graph?
body: <p>I have a simple graph like this:</p>
  
  <pre><code>(v1)---(v2)---(v3)---(v10)
   |      |      | 
  (v4)---(v5)---(v6)
   |      |      | 
  (v7)---(v8)---(v9)
  </code></pre>
  
  <p>I convert the game board into grids and each grid is a vertex and each vertex has a weight.
  Now I need an algorithm to find most weighted way between one vertex which can be one of vertices <strong>from (v1) to (v9)</strong> and another vertex is <strong>(v10)</strong>.</p>
  
  <p><strong>Example for vertices weight:</strong> Consider that each vertex weight is 1, so, If my path be <strong>(v1)->(v2)->(v3)->(v10)</strong>, my path weight will be 4.</p>
  
  <p>I already used BFS algorithm to find all possible paths, then calculate weights of proper paths (those paths which end with <strong>(v10)</strong>) between all paths. But BFS can't find all possible paths for me (maybe BF. However, I can use a trick for that, but I wonder if there is an algorithm for making my job easy and more efficient :).</p>