yeah can find a decent step by step guide to this on line. one that describes each detail of each step otherwise im not going to get it. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/84.203.48.54|84.203.48.54]] ([[User talk:84.203.48.54|talk]]) 19:53, 21 May 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
== Zero weight cycles ==
I seems to me that if a graph has some cycle that weighs zero between start and end, then there could be infinite shortest paths. If this is correct, then the correctnes proof should be rewritten a little so that it states all the cases. --[[User:Hdante|Hdante]] 18:40, 7 November 2005 (UTC)
From what I understand, there may be many more than a single shortest path (think of two equal routes), and Bellman-Ford is guaranteed to find one of them. Thus an infinite number of equal shortest paths is not a problem. The issue with negative weight cycles is that you can always find a better path by adding one more cycle to the path and as such there is no shortest path. [[User:Kyeprime|kyeprime]] ([[User talk:Kyeprime|talk]]) 19:17, 21 April 2010 (UTC)
In every finite graph, there is only a finite number of paths, because no path may visit a vertex or an edge twice. Therefore, there is only a finite number of shortest paths, too. However, finding a shortest path in graphs with arbitrary edge-weights is NP-hard. [[User:Morgurth|Morgurth]] ([[User talk:Morgurth|talk]]) 12:13, 1 November 2011 (UTC)
Note: And with path, I mean simple path in the terminology that is used on Wikipedia. [[User:Morgurth|Morgurth]] ([[User talk:Morgurth|talk]]) 12:32, 1 November 2011 (UTC)
