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 approximate to 2.2(1), insensitive to different values of gamma in the range, 23, 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.