Why friends in common reveal network stars
2026-08-26
The Friendship Paradox states that, on average, your friends have more friends than you do. We extend this to common friends—those who appear in multiple people’s friend lists. We show that the more people who share a common friend, the more connected that person tends to be, and we derive an expression quantifying this progression. In a regional Facebook network, a common friend to three randomly sampled individuals has on average more friends than 99.9% of the network. In a citation network, a source cited by any two of a random sample of papers has on average more citations than 99.99% of cited works. This power of common friends is most pronounced when few nodes hold disproportionate shares of ties, typical of networks involving superspreaders of disease, mega-influencers online, and highly connected nodes in neural networks. We discuss implications for network sampling, targeted interventions, social perception, and network dynamics.