Thursday, January 8, 2026 - 16:00 in U2-232
The Friendship Paradox on Sparse Random Graphs and Random Trees
A talk in the Oberseminar Probability Theory and Mathematical Statistics series by
Azadeh Parvaneh from Leiden University
| Abstract: |
The friendship paradox is a structural bias in networks stating that, on average, the neighbours of a vertex tend to have a higher degree than the vertex itself. Although this is counterintuitive, the phenomenon is deeply rooted in the geometry of networks and holds for every finite (simple or multiple) graph. However, at the level of individual vertices, it is not a priori guaranteed that most vertices have a smaller degree than their neighbours. This observation led us to introduce the notion of "significance" of the friendship paradox. In this talk, we introduce a probabilistic framework for analysing the friendship paradox via the local limits of sparse random graphs. For trees, we classify vertices into three types—negative, neutral, or positive—according to their friendship bias. We then investigate the significance of the friendship paradox on trees, with particular emphasis on infinite Galton–Watson trees.
[Based on joint works with R.S. Hazra, F. den Hollander, and N. Litvak.]
Within the CRC this talk is associated to the project(s): B10 |
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