Scale-free networks and the friendship paradox
- What do degree distributions look like?
- In many cases, they are really skewed!
- A few people have many edges, while many have few
- Rich-get-richer processes (preferential attachment)
Why are they called scale-free?
- No matter where you zoom in on the distribution, it has the same shape
- Robust to random failures
- Outcomes are “unfair”
- Scott Feld (Purdue Sociologist!)
- On average, your friends have more friends than you do
- The key idea is that people who are connected to lots of people are more likely to show up in your friend network.
- You are likely to be friends with people who have lots of friends, because they have lots of friends!
- This is much more pronounced as the skew of a network changes
- E.g., the people you follow on Twitter/Instagram are likely much more popular than you
- In many cases, we can’t see who is most popular
- Simply choosing a node at random, and then choosing one of their friends will identify a group that is more popular and closer to center
- Detect outbreaks
- Focus interventions