Hi Karen,
I do not know how important it is for your project to use your own Facebook data, as opposed to someone else's. There is a website that contains large data sets, including some of Facebook. In a certain sense that might be even more useful than your own data, because it might be more representative. If you download the Facebook data from that website you can import and plot it like so:
Graph[#[[1]] -> #[[2]] & /@ (Flatten[StringSplit[#, " "], 2] & /@ Import["~/Desktop/facebook_combined.txt", "TSV"])]
(You might have to adapt the path to the file.) You can also identify communities, but the following command will run a couple of minutes:
CommunityGraphPlot[#[[1]] -> #[[2]] & /@ (Flatten[StringSplit[#, " "],2] & /@ Import["~/Desktop/facebook_combined.txt", "TSV"])]
Once you have the graph you can of course use Mathematica's rich functionality of graph analytics. By the way, if you do not want to save the file on your hard drive, you can also use the file from the Internet directly:
Graph[#[[1]] -> #[[2]] & /@ (Flatten[StringSplit[#, " "], 2] & /@ Import["https://snap.stanford.edu/data/facebook_combined.txt.gz", "TSV"])]
and
CommunityGraphPlot[#[[1]] -> #[[2]] & /@ (Flatten[StringSplit[#, " "],2] & /@ Import["https://snap.stanford.edu/data/facebook_combined.txt.gz", "TSV"])]
What I am trying to say is that even if the Facebook API does not work as before, there are fantastic data sets out there that you might work on. Mathematica offers all the tools to import the data and analyse it. In the Stanford website you find for example data from Google circles, that contains many more nodes and edges.
There are also really interesting posts by Stephen Wolfram such as Data Science of the Facebook World.
I am not sure if this helps,
Marco