You are probably aware that you have 1st, 2nd and 3rd Degree connections. Anyone outside of these is not in your network.
1st Degree Connections – these are anyone you’ve added to your network, you can message them directly. 2nd Degree Connections – anyone your 1st Degree connections knows plus any connections in groups you have joined.
Bonus Tip: It appears you can either Connect or Message 3rd degree connections – but a message is the Premium (paid for) option. Why do that when you can connect with them? This is as simple as hitting the Connect button and sending them a message.