Acceleratingly growing scale-free networks with tunable degree exponents

In this paper, we analytically study the probabilistic accelerating network [M.J. Gagen, J.S. Mattick, Phys. Rev. E 72 (2005) 016123] in its accelerating regimes by using mean field theory. In the growing network, the number of links added with each new node is a nonlinearly increasing function aNβ(t) where N(t) is the number of nodes present at time t. It is found that the network appears to have a power-law degree distribution for large degree with tunable degree exponents (ranging from 3.0 to theoretically infinity) and the degree exponent γ depends only on the parameter β as γ=1+21−β. The analytical results are found to be in good agreement with those obtained by extensive numerical simulations.