What do we do with the power-laws?
Most distribution of interest are skewed
Averages falsely imply a uniform distribution
- Ex: 85% on nodes in one data set had outdegree less than average
Exponents of power-laws manage to capture the trend of a property with one number
Useful for answering what-if questions: “What will be the diameter of the Internet if the number of nodes doubles?”
Can scrutinize the plausibility of a hypothesis if they contradict the power-laws
Use power-laws to characterize graph topologies. They can be used as a “qualifying exam” for the realism of a graph.