Benford’s Law and Dunbar’s Number: Does Facebook Have a Power to Change Natural and Anthropological Laws?

Abstract

This paper presents the SmartSocial Dataset which describes 1,826 Facebook users with lots of details, including their connections and their interactions (e.g., posts, likes, and comments). We first present a detailed analysis of descriptive and network characteristics of the SmartSocial Dataset to provide evidence for its representativeness. Afterward, we analyze the relationship between social and behavioral characteristics of SmartSocial Dataset users and Benford's Law as well as Dunbar's Number, to test whether Facebook has the power to change natural (Benford) and anthropological (Dunbar) laws. We find that Facebook's features are aligned with the Benford's Law but redefine the way how Dunbar's Number is calculated. Finally, we demonstrate how those findings could help researchers and business practitioners who collect Facebook data sets in a way to indicate whether there is serious sampling problem with the data set they collected.

Keywords

• Benford’s Law
• data analysis
• Dunbar’s Number
• Facebook
• SmartSocial Dataset
• social computing