Check out the (deliberately blurry) examples in https://arxiv.org/pdf/1703.05393.pdf where it can distinguish between blurred, low resolution pictures of different types of crows.
It's only ~50% accuracy, but the photos are terrible. Much worse than Facebook pics.
OTOH, this is classification into hundreds of classes, not millions like in the case of FB face recognition. (Although of course that can use the connectivity graph as a filter on that too).
If you wanted a general algorithm working on non-curated data (like tagging facebook photos for instance) I'm sure it would be significantly harder.