No, that is not barbed wire. The three runs of wire up to, attached to the barb wire arms, is actually bottom coil wire. It was installed to deter the dogs from climbing out of their fenced area.
This fence used residential specifications except that the top rail was 1-5/8 x .055 instead of the typical 1-3/8 x .055 top rail as to accept the barb wire arms. The gate also, was a 1-5/8 x .055 frame.