Why friends in common reveal network stars

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.