Benford’s Law Applies to Online Social Networks

Fake social media accounts and Russian meddling in US elections have been in the news lately, with Mark Zuckerberg (Facebook founder) testifying this week before the US Congress. Dr. Jen Golbeck , who teaches Network Analysis at Statistics.com, published an ingenious way to determine whether a Facebook, Twitter or other social media account is fraudulent.

Her paper came out in 2015, but is worth revisiting. Using the results from this research, Golbeck and others published a list of fake Russian Twitter accounts three years ago, and the fake accounts were still active at the beginning of 2018.

Golbeck counted up the “friends of friends” for each user’s friend (i.e., for a given user, how many friends does her first friend have, how many does her second friend have, and so on). She found that the resulting distribution of counts is one of the datasets that obeys Benford’s Law, i.e. 30% of the first digits were 1’s, 18% were 2’s, etc. (see frequency distribution to right). Except for a small percentage of users that did not conform to Benford’s Law – they turned out to be the fake Russian accounts.