Get mutual Facebook friends with an application BEFORE installing app

Is it possible to get mutual friends between me and an application or page programmatically?

For example:

In the above picture you can clearly see that before installing Causes App (1) I can see that me and Causes App hav开发者_运维知识库e 818 mutual friends (2) or 818 of my friends are using Causes Application.

Is it possible to somehow get this relationship programmatically for applications that I haven't installed yet?

I'm sorry, but the answer is no. That feature is internal to Facebook and without installing the application, and implementing the necessary extended permissions, your application just won't have access to the required data to produce this kind information.