Is there an implementation of prim's algorithm or any other algorithm in geotools graph package for solving the minimum spanning tree problem?
The short answer is no, it is not implemented. But from a quick look at the algorithm it should be possible to implement in GeoTools' graph module. Check out the code in org.geotools.graph.traverse and org.geotools.graph.traverse.standard.
If you get one working the PR's are always welcome.