Well, the thing is, it is still not OK. I really don't want to make this too hard, but ideally what I want is a piece of _self-contained_ code, that I can just copy and paste into an R session. Reading files is OK, but I still had to edit the file name and complete your code to make it run. And your code in the last email is not the same as in the first.
These might seem small things to you, but it took me ~10 minutes to check your problem. If you send self-contained code, it takes 1 minute, or less and I would have probably replied earlier, I just did not have ~20 minutes for this. Don't take this personally, please, sending good bug reports is a skill. OK, enough ranting for today.
So it seems like the problem is that when you write 'weighted=NULL' for graph.adjacency(), and your data is not binary but contains some larger numbers as well, it will create a network with multiple edges, i.e. 4 in your adjacency matrix creates 4 edges between the vertices. This might not be the best default behavior, but this is how it is.
If you want to get rid of the multiple edges, call simplify() on the graph.
Best,
Gabor