Evolution of networks with aging of sites

We study the growth of a network with aging of sites. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the Barabasi-Albert's model and (ii) to tau(-alpha), where tau is the age of the old site. We find both from simulation and analytically that the network shows scaling behavior only in the region alpha<1. When alpha increases from -infinity to 0, the exponent gamma of the distribution of connectivities [P(k) approximately k(-gamma) for large k] grows from 2 to the value for the network without aging. The ensuing increase of alpha to 1 causes gamma to grow to infinity. For alpha>1, the distribution P(k) is exponentional.