Transfer files from one computer to another using Skype Server

I have two computers at home. Computer A and Computer B are on the same wireless network. If both are running Skype, and I transfer a file from one computer to another using Skype, does the first computer upload the content to a Skype server and the second computer downloads it from the Skype server?
Or, does Skype just use the router in place to transfer the file?
Thanks.
