Router

i was just wondering about routers.
We have a cisco router at work. We use NT4.
We have a Sydney office, Melbourne, Adelaide and Brisbane.
We have a direct link to Melbourne and Brisbane but not to Adelaide from Sydney.
We are going to put a direct link to Adelaide aswell.
Does this mean that this is another physical connection to the router so that now we will have 3 cables coming out of the router rather then 2 for the new link??