Universal Behavior of Load Distribution in Scale-free Networks
Abstract
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.