Wrong action:

When you send a LinkedIn invitation to join someone's network.  Never say that you are a friend if you are not.  People will only delete your invite because they believe you are a dishonest person trying to get into their network. 

Correct action:

Send a message stating that you would like to get to know the person.  There are two ways this can be achieved:

1. If the person is in your network circle, ask a friend or other network contact to introduce you.

2.  If the person is not in your network, join a group that the person is a member of.  This will give you access to send a message.