I\'m now working on a web application which is mostly based of facebook graph api. I hold some data about users - actually , the possible public data available - such as nam
This will be helpful link:
http://graph.facebook.com/893914824028397/picture?type=large&redirect=true&width=500&height=500
You can set height and width as you needed
893914824028397 is facebookid
you can get it with using this url : you will get the picture HD (max size)
https://graph.facebook.com/{userID}?fields=picture.width(720).height(720)&redirect=false
don't forget redirect=false or it will return an error
Here, this api allows you to get fb, google and twitter profile pics easily
https://www.avatars.io/
It's an API that returns the profile image when given a username for a variety of social networks including Twitter, Facebook, Instagram, and gravatar. It has libraries for iOS, Android, Ruby, Node, PHP, Python, and JavaScript.