Zero insert size means :
1. mate unmapped. (or)
2. Multi mapped read. (or)
3. Mate mapped to different 'Chr/scaffold/contig'
And may be others, but its good to look at the flag (column 2) and check whats happening.
I am not sure If I understand you right but this is the histogram I am talking about
so Do i need to see all the sam file flags?
<font size="2">What genome are you working with ? If the genome that you have used for reference mapping is not assembled into Chromosomes, with mate pair data, this may be possible, as the two pairs of a read mapped to different contigs/scaffolds as mate pair will have large inserts (3kb/5kb/10kb). Hence, it is normal to </font>have zero insert size <font size="2">for a mate pair data aligned to a draft genome.</font>
But, could you let me know whats the size of the mate pair fragment during library prep ?
Library size is 8 kb . and this big zero column i could not explain it , so according to your answer shall I count it as pairs that mapped to different locus?! or you have other suggestion? could it be library preparation problem?