Right now the Facebook API is returning a URL like this with all post/album images 130x130 pixels in size:
https://fbcdn-sphotos-h-a.akamaihd.net/hpho
https://graph.facebook.com/{object_id}/picture?type={thumbnail|album|normal}
Example (using a bogus object_id of 122233334444555):
https://graph.facebook.com/122233334444555/picture?picture?type=large
Make sure object_id is not just the id of an item but it's object_id
(which is typically the number following the underscore in the full id).
I got those type values from a helpful facebook response message that said:
"message": "(#100) type must be one of the following values: thumbnail, album, normal"
In place of ?type=... you could do height/width as well:
?width=543&height=543
After a couple of hours searching and pulling my hair out, I found a solution that works for me. In my case I'm pulling posts from {page-id}/posts, but I'm pretty sure this will work for you too, seeing that I used to get larger images using the same approach as you mention.
This is works for me:
bigger_image="https://graph.facebook.com/" + picture_url_from_facebook.match(/_\d+/)[0].slice(1) + "/picture?type=normal";
You can see this working in action @ this fiddle or this page we did for a client
Thanks to Er Adhish for leading the way to the solution @ https://stackoverflow.com/a/27075503/2908761