Kolloquium: Frank den Hollander (Universiteit Leiden): „The Friendship Paradox in Social Networks“

The Friendship Paradox in Social Networks – Vortragender: Frank den Hollander, Universiteit Leiden – Einladender: A. Greven

Abstract: Consider
a group of individuals who form a social network. For each individual in the
group, compute the di_erence 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 _rst
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 quanti_ed, and illustrate it with two examples. We also look at
the multi-level friendship
paradox, where friends are
selected according to an exploration
process. We show that di_erent
types of scaling can occur as the size of the graph and the depth of the
exploration tend to in_nity jointly.
Based on joint work with R.S. Hazra and A. Parvaneh.