LinkedIn is not just a business network where you create a profile just to have a presence and then ignore it. LI is a lot like Facebook, where you can join groups and participate. Do a search for writer and/or publisher groups to network with and learn from each other. Search for groups revolving around interests pertinent to your book theme or topic and participate as a involved member, not as an author. There you may mention your book casually in pertinent conversation, and group members who want to find out more about you because they like your comments can simply click onto your profile and discover you have a book. Either way, do not spam by repeatedly posting sales pitches for your book. Patrick Dorsey, a member of our SLPA LinkedIn group, shared the following article:
The REAL Power of LinkedIn for Authors
There are many more writer groups than this article mentions, so search away!