As a man with a BSc in a computer science who hopes to get a MA in ancient history this December, and who briefly read their article, I can say that their methodology is confused. For example, they don't have a group of historical narratives as a control group, they don't consider that the social network in the Homeric tradition is different than that in any fragment such as the
Iliad, and they don't explain why
Richard III counts as a fictional narrative not a historical one. (Of course its not very truthful history ... but even to a strong believer in their historicity neither are
Beowulf or the
Iliad). In other words, it doesn't really prove anything. To do that they would have to have two control groups (fictional and historical narratives), compare the social networks in a given text to each group and see which it resembled, then ask literary scholars why that might be.
Despite the note on p. 2, I would also be interested to see some worked examples of how they divided relationships into friendly and hostile. Do Glaucus and Diomedes count as friendly (they are guest-friends) or hostile (they try to kill each other)? What about Paris and Menelaus? Achilles and Agamemnon? What models of "real social networks" do they use and why would social networks in warlike Iron Age societies organized by family ties be similar? (Their bibliography doesn't have article titles, just authors, dates, and journals, so one would have to read their sources to get an idea).
Richard Carrier has a detailed critique from a classicist's perspective (
“Bad Science Proves Demigods Exist!”). I have to agree that this reflects poorly on the authors' and reviewers' practical knowledge of logic. It is an intriguing approach though, and its possible that one day there will be evidence that it is useful.