I am looking for an algorithm to render network nodes and their
connections into a diagram with the fewest number of "overlapping"
connections. The algorithm would need to position the nodes and their
connections given an array of node connections (this could be
presented to the algorithm by whichever means necessary). The
resulting diagram should be easy for humans to interpret (ie. all
nodes evenly placed apart and the map somewhat centered). I am sure
there are some examples on the expansive world wide web somewhere, but
my google searches have come up with nothing so far.

A coded example would be nice, but not essential.