Facebook graph API tells me I can get a profile picture of a user using
http://graph.facebook.com/517267866/picture?type=large
which works fine. However, whe
I realize this is late, but there is another way to obtain the URL of the profile image.
To your original url, you can add the parameter redirect=false to obtain the actual URL of the image you'd normally be redirected to.
So, the new request would look like http://graph.facebook.com/517267866/picture?type=large&redirect=false. This will return a JSON object containing the URL of the picture and a boolean is_silhouette (true if the picture is the default Facebook picture).
The picture will be of the size you specified, as well. You can test this additionally by adding dimensions: http://graph.facebook.com/517267866/picture?type=large&redirect=false&width=400&height=400