The rank exponent: R
Take the nodes of a graph sorted in decreasing order by outdegree and plot (rank, outdegree) in log-log scale.
Power-law 1 (rank exponent): The outdegree, dv, of a node v, is proportional to its rank, rv, to the power of a constant, R:
- dv is proportional to rvR
Definition: Define the rank exponent, R, as the slope of the plot of the outdegrees of the nodes versus the rank of the nodes in log-log scale. Intuitively, Power-law 1 most likely reflects a principle of the way domains connect
Exponent Top1 Top2 Top3 Top4 rank -0.81 -0.82 -0.74 -0.48
One Application: used to estimate |E| given N and R.