Can't you configure what gets delivered as a notification? If you're so popular that people are adding you to circles all the time, can't you just turn those notifications off?
As far as I can tell, you can customize email and phone notifications, but you can't customize the notifications that appear under the red alert number on Google web pages. (I might be missing something.)
There's a "Who can send you notifications?" section on the settings page which allows you to configure who can send you notifications that trigger the red alert.