A 2D Layout Algorithm for Small, Sparse, and Undirected Graphs with a Specific Edge Length I would like to to draw a graph where every edge $e_m$ has a predefined length of $l$. Given that the graph is small and sparse, it should be feasable. However, I did not manage to find an algorithm which does this (or one that is suitable to modify) yet I'm sure that this is a solved problem. Does anyone know of such a layout algorithm and could point me to an implementation or paper?
"Planar Embeddings of Graphs with Specified Edge Lengths" by Cabello, Demaine, and Rote (or one of the references they cite) seems to solve your problem.

If you don't care about edges crossing too much, a simple heuristic approach could be gradient descent. Start with a random position and iteratively wiggle the nodes a bit to decrease the sum of differences of the current edge lengths to your desired lengths.