Friendship Paradox Sampling

The Friendship Paradox states that, on average, most people's friends have more friends than they do. This counterintuitive phenomenon arises from a sampling bias: people with many friends are (by definition) more likely to be your friend, making them overrepresented when we sample average degrees across friendship connections.

Experiment

Explore different network structures by manipulating the controls in the interactive visualization:

1. Select the Path graph and set Person ID to 1. Notice how the population mean degree and edge endpoint mean degree change compared to the star graph. Person 1 has a degree of 2, while their friends have an average degree of 1.5.
2. Change the graph to Complete. In a fully connected network, every person is identical in terms of degree (everyone has 4 friends). Observe that the population mean, edge endpoint mean, and local mean are all perfectly equal to 4.0. The paradox only emerges when there is variance in the degree distribution.
3. Try the Isolates or Empty graph configurations. When a person has no friends, their local neighbor mean becomes unavailable. The uniform active person local mean properly excludes isolated people instead of treating them as having 0-degree friends.

You can interact directly with the module here: Friendship Paradox Sampling.