Consider a group of individuals who form a social network. For each individual in the group, compute the difference between the average number of friends of friends and the number of friends (all friendships are mutual), and average these numbers over all the individuals in the group. It turns out that the latter average is always non-negative, and is strictly positive as soon as not all individuals have exactly the same number of friends. This bias, which at first glance seems counterintuitive, goes under the name of friendship paradox, even though it is a hard fact. In this talk we model the social network as a sparse random graph. We explain where the bias comes from, how it can be quantified, and illustrate it with two examples. We also look at the multi-level friendship paradox, where friends are selected accord- ing to an exploration process. We show that different types of scaling may or may not occur as the size of the graph and the depth of the exploration tend to infinity jointly.
Based on joint work with R.S. Hazra and A. Parvaneh.
Zoom Link: https://us02web.zoom.us/j/88670406480
Meeting ID: 886 7040 6480
This is part of the Bangalore Probability Seminar Series. For details of past and upcoming seminars kindly see Link