Universal Behavior of Load Distribution in Scale-free Networks

We study a problem of data packet transport in scale-free networks whose degree distribution follows a power-law with the exponent $\gamma$. We define load at each vertex as the accumulated total number of data packets passing through that vertex when every pair of vertices send and receive a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power-law with the exponent $\delta \approx 2.2(1)$, insensitive to different values of $\gamma$ in the range, $2 < \gamma \le 3$, and different mean degrees, which is valid for both undirected and directed cases. Thus, we conjecture that the load exponent is a universal quantity to characterize scale-free networks.