Network Weirdness: Exploring the Origins of Network Paradoxes
  Social networks have many counter-intuitive properties, including the "friendship paradox" that states, on average, your friends have more friends than you do. Recently, a variety of other paradoxes were demonstrated in online social networks. This paper explores the origins of these network paradoxes. Specifically, we ask whether they arise from mathematical properties of the networks or whether they have a behavioral origin. We show that sampling from heavy-tailed distributions always gives rise to a paradox in the mean, but not the median. We propose a strong form of network paradoxes, based on utilizing the median, and validate it empirically using data from two online social networks. Specifically, we show that for any user the majority of user's friends and followers have more friends, followers, etc. than the user, and that this cannot be explained by statistical properties of sampling. Next, we explore the behavioral origins of the paradoxes by using the shuffle test to remove correlations between node degrees and attributes. We find that paradoxes for the mean persist in the shuffled network, but not for the median. We demonstrate that strong paradoxes arise due to the assortativity of user attributes, including degree, and correlation between degree and attribute. 
Farshad Kooti, Nathan O. Hodas, Kristina Lerman
cs.SI cs.CY physics.soc-ph