The Number of Paths in a Directed Graph
That's not true even for DAGs: consider the following, with all edges directed left-to-right:

  o   o   o ... o
 / \ / \ /       \
x   o   o   ...   y
 \ / \ / \       /
  o   o   o ... o


There are $2^{|E|/4}$ paths from $x$ to&nbsp;$y$. In a graph with cycles, it can be even worse: consider a clique.