Counterexample to max-flow algorithms with irrational weights?
The answer is that for every irrational number $r$, there exists a network 


with $n=6$ vertices and $m=8$ arcs,
in which seven arcs have integer capacity,
in which one arc has capacity $r$,
and on which Ford-Fulkerson may fail to terminate.


This has been proved in the paper


  Toshihiko Takahashi:
  "The Simplest and Smallest Network on Which the Ford-Fulkerson Maximum Flow Procedure May Fail to Terminate"
  Journal of Information Processing 24, pp 390-394, 2016.
  Link: https://www.jstage.jst.go.jp/article/ipsjjip/24/2/24_390/_article