The hop-plot exponent: H
Want to quantify the connectivity and distances between Internet nodes
Novel way: study the size of the neighborhood within some distance instead of the distance itself.
Use P(h), the total number of pairs of nodes within less or equal to h hops (including self-pairs and each other pair counted twice)
Approximation (hop-plot exponent): P(h) is proportional to the number of hops to the power of a constant, H:
- P(h) is proportional to hH, for h << d
Exponent Top1 Top2 Top3 Top4 hop-plot 4.62 4.71 4.86 2.83
Application: use H, N and E to define def, the effective diameter of the network: any two nodes are within def hops from each other with high probability.