The Short Version:
"I can visit the public page without being logged into Facebook and see underneath the post is says "2155 shares" I would like to know how to access that number through the API"
The Details:
I'm trying to use the newest version (v2.5) of the graph HTTP API to determine the total share count for a public video. The problem is FB seems to have changed the API enough that older posts on SO no longer answer this question.
Looking at the Graph API Documentation it appears that video nodes now have the "sharedposts" edge. However, calling this route with summary=true only returns a few of the shares and no value for a total count. This returns counts for comments and likes so I'm not using the endpoints incorrectly or messing up my authorization.
I've also tried to use the URL Node but this doesn't seem to do much with links inside of Facebook. I simply get a JSON response with an 'id' field with the same url I supplied as a request parameter. Seems like this route is meant to be used for links to content outside of Facebook.
I've tried the above methods with multiple videos on multiple public pages so I don't think it is due to the group owners restricting access, unless this is the new default.
It seems arbitrary that I would be allowed access to total counts for comments and likes, but not shares. Is there some legacy way to do this or am I out of luck for now?