Packet transport along the shortest pathways in scale-free networks

Abstract

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 Barabasi-Albert-type model that the exponent \(\delta\) changes abruptly from \(\delta = 2.0\) for tree structure to \(\delta\simeq2.2\) as the number of loops increases. The load exponent seems to be insensitive to different values of the degree exponent \(\gamma\) as long as \(2 < \gamma < 3\).