• Your LinkedIn network consists of your first-, second-, and third-degree connections, as well as your followers and fellow members of LinkedIn groups. You can expand your network by inviting other LinkedIn members and contacts you've imported to connect with you, or by accepting invitations from others. The degree of connection you have with another LinkedIn member has an impact on how you can communicate with them.
• Some private profile results are simply people who aren't in your network - they haven't opted to keep their LinkedIn profile off the web – but they nevertheless show up as 'private' results because you aren't connected to them.

Read More: Can you tell if someone removes you from LinkedIn?