That depressing idea that all your friends are more popular than you might just be a simple math error.
arXiv · March 18, 2026 · 2603.16337
The Takeaway
The 'friendship paradox' is a famous rule in social science stating that, on average, your friends have more friends than you do. This paper mathematically proves that the paradox completely disappears if you change how you sample the network, suggesting the feeling of being less popular is just a result of how we collect data.
From the abstract
We show that in an undirected graph under degree biased sampling the expected degree of vertices is equal to the expected degree of their neighbors. In consequence, under the biased sampling the social network result known as the friendship paradox disappears. The identity is equivalent to the existence of a stationary state of a random walk on the graph or to the conservation of the total flow defined by the difference of the degrees of the vertices.