Hi Antonio, I did not mean to confuse you. I'll try to explain again:
Velvet reports the coverage in two files: the Log file (Median Coverage Depth) and the contigs.fa file (in each contigs header, preceded by _cov_). Assuming both of these are kmer coverages, I supposed the median of the coverages in the contigs.fa file should be equal to the median coverage in the Log file, but it wasn't.
I then supposed that the median coverage in the Log file could be in terms of nucleotides, so I converted the coverages in the contigs.fa file into nucleotide coverages (by multiplying by (L / (L - k + 1))) and found their median. This median was again different than that reported in the Log file.
This made me confused, as you are, as to what the coverages reported in contigs.fa and the median coverage reported in the Log file actually mean, so I asked the wise online bioinformatics community for enlightenment.
It's not normal coverage, it's nucleotide coverage (C). You need to rearrange the formula to find C based on all the other info.
That's what I did. The problem is that the median C I found is different than the C reported by velvet in the Log file as "Median coverage depth."