Your team is made up of people you pay to work with you.
Your network is made up of people who are looking out for your interests (and you for theirs) even though there is no formal agreement among you.
Some members of your team will become part of your network.
Some members of your network will at times join your team.
You treat them the same. Get to know them. Understand what they want and what motivates them. Help them get what they want by introducing them to people that you know.
If you want to discuss teams and networking in further detail (including how to get better results from your team and better leads from your network), feel free to set up a call.