story identification - Need title of book I read in the 80's about a post-apocalyptic earth in which all humans are telepathic

Back in the late 70's or early-to-mid-80's I bought a book from the Science Fiction Book Club about a post-apocalyptic Earth in which people lived in small villages and everyone was telepathic - they all connected to a shared “Net” so it’s more like a hive mind than simple telepathy. You can shield your private thoughts, and in fact you are required to do this much of the time to avoid bothering people, but everyone knows when you are doing this. Occasionally a baby is born that is lacking telepathy, and it is seen as a helpless deviant and killed immediately. When young people are 12 or 13 they must go through an initiation in which they are sent out into the wilderness for several days, but they have no idea what will happen to them because it is forbidden to talk about it and this info is shielded from the Net. What happens is they are cut off from the Net for a few days, and how they deal with this is their initiation into adult life. Some commit suicide because they can’t handle the mental isolation. The book is narrated by a young girl who is about to face her initiation.

If anyone can tell me what the name of this book is I would very much appreciate it, because I want to recommend it to some young relatives.