Benford’s Law states that, in naturally occurring systems, the frequency of numbers’ first digits is not evenly distributed. Numbers beginning with a 1 occur roughly 30 of the time, and are six times more common than numbers beginning with a 9. We show that Benford’s Law applies to social and behavioral features of users in online social networks. Using social data from five major social networks (Facebook, Twitter, Google Plus, Pinterest, and LiveJournal), we show that the distribution of first significant digits of friend and follower counts for users in these systems follow Benford’s Law. The same is true for the number of posts users make. We extend this to egocentric networks, showing that friend counts among the people in an individual’s social network also follows the expected distribution. We discuss how this can be used to detect suspicious or fraudulent activity online and to validate datasets.
@cite_3: When we examine numbers in the newspaper or magazines we might expect that their first digits are just as likely to be 8 or 9 as a 1 or a 2 and we might assume that each of the nine digits (zero is not used as a first digit of course) will occur 1 9 of the time. Unexpectedly this turns out to be untrue in many situations.
The formula for the law, @math , provides a theoretical distribution of expected first digits, shown in Table 1. On the surface, Benford's Law is quite counter-intuitive. Why would numbers beginning with 1 be any more common than those beginning with 9? However, the law holds across many variations in measurement @cite_3 . Temperatures that follow Benford's Law do so regardless of whether they are measured in Farenheit, Celsius, or Kelvin. Distances follow whether measured in miles, kilometers, or smoots.