Yes, the publish rights are:

Everyone public
Network protected
Contacts private
Individuals private

OR
Create a customized access list by selecting any combination of the people listed below.

People who are in your Network:
Your friends, their friends, and their friends
Your family members, their family members, and their family members
Your professional contacts, their prof. contacts, and their prof. contacts

People who are your Contacts:
Your friends who have a direct connection to you
Your online buddies
Your family members who have a direct connection to you
Your professional contacts who have a direct connection to you