Packet transport along the shortest pathways in scale-free networks

We investigate a problem of data packet transport between a pair of vertices on scale-free networks without loops or with a small number of loops. By introducing load of a vertex as accumulated sum of a fraction of data packets traveling along the shortest pathways between every pair of vertices, it is found that the load distribution follows a power law with an exponent ??. It is found for the Barabasi-Albert-type model that the exponent ?? changes abruptly from ?? = 2.0 for tree structure to ?? ≃ as the number of loops increases. The load exponent seems to be insensitive to different values of the degree exponent ?? as long as 2 < ?? < 3.close192