title: Why need (node number - 1) iterations in Bellman Ford algorithm to find shortest paths?
body: <p><a href="https://i.stack.imgur.com/jOhJW.png" rel="noreferrer"><img src="https://i.stack.imgur.com/jOhJW.png" alt="enter image description here"></a></p>
  
  <p>Image: 4 iterations, with (a) is the original graph. (b), (c), (d), (e) correspond to result after each iteration. Example from "Introduction to Algorithm 3rd"</p>
  
  <p>Hi, 
  I do not understand few aspects about the algorithm. I hope someone could help. Below are my questions.</p>
  
  <p>In each iteration, all edges are relaxed, as far as I concern. I expected all the node are updated distance in the first iteration. So why in the first iteration (b), only distance of node t and y are updated but the other still infinity?  </p>
  
  <p>Another question is, why need (node number - 1) iterations in which all edges are relaxed? What is guaranteed to achieve at each iteration so that the algorithm must run in (node number - 1) time to make sure the shortest path is found as long as no negative-weight cycles exist?</p>