Searching for business contacts on LinkedIn can be thought of as joining two moviestars via Kevin Bacon, center of the entertainment universe. Except with LinkedIn, you are limited to three degrees of separation and not six.
The people within that 3-degree universe (your LinkedIn network) represent the sum total of your direct connections, plus their connections, and so on to three levels. If a contact is outside that your network, you can only see their title on their profile, not their full name.
Let's experiment with the effect each connection you create brings to the size and scope of your network.