Facebook social network analysis on my page's comments/shares/likes - facebook

Question

Let me explain the whole thing here so you can have a clear picture of the situation:
I have a page on facebook and the insights (both on the page and from the graph api) give me a lot of valuable information, but I need to go deeper. I was thinking of applying the social network analysis concepts (centrality, betweenness, eigenvector, etc) on who likes/shares/comments on my pages posts/pics/etc, so I can find the key-users of my page and how virality spreads among them.
Lets take 'liking a post' as an example. First thing I need is to get a list of everyone who liked that post, which is simple and can be done with a few requests to the graphapi. Now comes the tricky part: I need to know the relationship between all these people who liked the post, but I don't have access to their friendlist. To have access to the friend list I'd have to make the page an app and request that permission, which can't be done at this point. But facebook api allows you to check if two individuals (user1 and user2) are friends with a request like this: user1/friends/user2, and for that I don't need special permissions, just a regular token. Well, so far so good, I just get the users who liked the post and check two-by-two which ones are friends. But here comes the problem:
I can make batch requests to the API, which means I can check 50 pairs of users with one request. And from what I read, facebook allows 600 requests each 600 seconds. Simple math: 30,000 pairs of users each 10 minutes. It's a big number, should be enough. It isn't. Let's assume that the post has 1,000 likes (not being optimistic at all). I'd have to check user1 against the other 999 users. Now user2 would have to be checked against the remaining 998 users (no need to check against user1 again, because the friend-check works both ways). User3 against 997 users and so on, until user999 needs to be checked against 1 user. Therefore I'd need to perform 999+998+997+996+...+3+2+1 checks, or 499,500 requests, which means almost 3 hours to get the data obeying facebook limitations. 10k likes would take over a week!
So my question is: is there any other way to make this work? Another way of getting data, or a largest batch request? Some way I can retrieve this data? Or it's just impossible, since facebook retains the important information?
Thank you for reading all this and helping me out ;)

Answer 1

What you are trying to get to is information that Facebook does not want easily available.
In the same way that you don't have access to "friends of friends", trying to reconstruct social connections takes far too many calls to the API since, as you stated, you would need to test against individual pairs.
Whilst your question is valid and from what I can tell you are not trying to obtain this data to to perform some malicious actions, I'm afraid that at this point you'll just have to use the data that Facebook makes available to you through the Insights application and the access to that data though the API as well.