Shortest paths and load scaling in scale-free trees
The distribution of the shortest path lengths and the load scaling in scale-free random trees was discussed. It was shown that, after dividing by N (the number of nodes), the load distribution converged to an integer distribution. It was observed that the bulk of the distribution was at log N. It was found that the distribution was asymptotically normal, with mean and variance log N/2.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Bollobás, B., & Riordan, O. (2004). Shortest paths and load scaling in scale-free trees. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 69 (3 2) https://doi.org/10.1103/PhysRevE.69.036114