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 $\gamma$. Load, or “betweenness centrality,” of a vertex is the accumulated total number of data packets passing through that vertex when every pair of vertices sends and receives a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power law with the exponent $\delta \approx 2.2\left(1\right)$, insensitive to different values of $\gamma$ in the range, $2<\mathrm{}\gamma \le 3$, 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.