Facebook’s real-time updates allow us to declare our interest in certain information about our users and have Facebook notify us when it changes instead of us continually querying the API. [...] There are of course other uses for real-time updates – and indeed we’ll take a look at one in this article: an example application which emails people when others “unfriend” them. (Actually that’s not strictly true – it tells you when someone is no longer your “friend” regardless of who did the unfriending.)
He helps you get everything you'll need installed (via Composer) including the Facebook SDK, PHPMailer for emails and Underscore for output handling. The sample interface uses a Slim-based structure (a PHP microframework) to make a callback URL that the Facebook application uses for it's real-time notifications. There's also an endpoint that's called when people allow the application access to their accounts, complete with the redirect URL. They show you how to handle the incoming JSON message from Facebook and how to create the email contents and send it out.