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I am looking for an algorithm that distributes nodes on a plane, such that the edges are
all the same size. I think it is by Dijkstra, but I cannot remember.
Anyone heard of this algorithm?
In general this will be impossible. Effectively you want something similar to the finite pictures in tilings of the plane.
There are some simple cases – regular polygons and a few graphs which include joined polygons, but even something as simple as the complete graph for 4 points (tetrahedron) is impossible.
If you want something that tries to balance the impossible constraints, try graphviz and its neato program.