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 delta. It is found for the Barabaasi-Albert-type model that the exponent delta changes abruptly from delta = 2.0 for tree structure to delta similar or equal to 2.2 as the number of loops increases. The load exponent seems to be insensitive to different values of the degree exponent gamma as long as 2 < gamma < 3.