I've looked after a widget that could pull a list of page titles (the thumbnail would be an extra), arranged on the number of FB likes they received.
I've tested some examples that promised to do that, added a custom field in the database for each article, but failed. There must be a way to pull that information for the api of FB.
Here is the page of a newspaper that does what I want, but I have no idea how they did it:
The widget I'm talking about is right bellow the large picture of the main article, in the box in the middle column.