Size-dependent degree distribution of a scale-free growing network - art. no. 062101

We propose the simplest model of scale-free growing networks and obtain the exact form of its degree distribution for any size of the network (degree is a number of connections of a node). We demonstrate that a trace of initi al conditions-a hump near cutoff of the degree distribution at k(cut)-t(bet a)-may be found for any network size. Here beta =1/(gamma -1), where gamma is the exponent of the degree distribution of the network. These size effec ts implement a natural boundary for the observation of the scale-free netwo rks.