Lecture
LCN2 seminar May 2024
- Date
- Friday 31 May 2024
- Time
- Location
- Gorlaeus
- Room
- BM. 2.26 (second floor)
66th LCN2 seminar
Speaker: Azadeh Parvaneh Ziabari (MI)
Title: The friendship paradox for sparse random graphs
Abstract:
In 1991, the American sociologist Scott Feld discovered the paradoxical phenomenon that 'your friends are more popular than you are'. This statement means the following. 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 of each connected friendship group 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 lecture we model the social network as a sparse random graph. We explain where the bias comes from, how it can be quantified, and illustrate our findings with two examples.
Based on joint work with Rajat Subhra Hazra and Frank den Hollander