On the Friendship Paradox and Inversity: A Network Property with Applications to Privacy-sensitive Network Interventions

Networks across many different settings—including social, economic, and natural—are powerful tools for interventions due to the cascading impact of one individual node on others. All networks with degree variation exhibit the friendship paradox phenomenon. We demonstrate its multifaceted nature, and provide its foundations mathematically and empirically. We identify a network property—inversity—and propose network intervention strategies based on the friendship paradox. Inversity uniquely determines the best-performing strategy. These strategies provide a privacy-sensitive approach to obtaining highly connected individuals without knowing the network, and are guaranteed to obtain a greater than average degree for almost any network. Finally, we characterize the value of these strategies theoretically and with real-world networks.