title: Finding path with maximum minimum capacity in graph
body: <p>I am helping a friend with a work related project where, he needs to calculate the maximum capacity from a node a to a node b, where the edge has a capacity. However the maximum capacity in a path from a to b is limited by the edge with the lowest capacity.</p>
  
  <p>Let me try to explain with a simple sample
  <img src="https://i.stack.imgur.com/Ay1pV.png" alt="Simple sample graph"></p>
  
  <p>So the graph is a directed graph with weighted edges, and it can be cyclic. The path with the highest capacity would be s->b->t and have the capacity of 250, since that edge is setting the limit.</p>
  
  <p>I have done a bit of reading and found out that this type of problem is a <a href="https://en.wikipedia.org/wiki/Widest_path_problem" rel="noreferrer">"Widest path problem"</a> or I would call it something like a path with maximum minimum capacity, but I haven't found any examples or any pseudo code explaining how to tackle this.</p>
  
  <p>I was thinking something in the lines of finding all paths from s to t, using BFS and somehow only to allow visiting a node once in a path, and then find the minimum value in the path, would that work?</p>