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 δ. It is found for the Barabási-Albert-type model that the exponent δ changes abruptly from δ = 2.0 for tree structure to δ ≃ as the number of loops increases. The load exponent seems to be insensitive to different values of the degree exponent γ as long as 2 < γ < 3.