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I often use

FindPath[G, 1, 2, {L}, All]

where $G$ is some graph. This finds all paths of length exactly $L$ edges which run between nodes $1$ and $2$.

In large graphs this is very slow.

One solution is to (I think) use Depth-Limited-Search starting at node $1$, of depth $L$.

I there an efficient way of doing this in Mathematica?

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