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 γ. 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 δ ≈ 2.2(1), insensitive to different values of γ in the range, 2 < γ ≤ 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.