Are there *practical* ways to construct the Szemerédi partitions of a given graph (on a computer)? I found this algorithmic version of the lemma (also see the references within), but I was unable to find any implementations, so I am wondering if these algorithms are practical at all.

Please note that I am not a mathematician and I am very new to this topic. I am trying to find out if it this will be useful for me. I was hoping that someone familiar with the field will be able to provide some guidance and help avoid a likely blind alley.

Also, can partitioning the graph like this recursively be used to define/compute a vertex ordering (ordering = labelling by natural numbers), so that the vertices in the same partition will be adjacent in the ordering?