Effect of the accelerating growth of communications networks on their structure

Motivated by data on the evolution of the Internet and World Wide Web we consider scenarios of self-organization of nonlinearly growing networks into free-scale structures. We find that the accelerating growth of networks establishes their structure. For growing networks with preferential linking and increasing density of links, two scenarios are possible. In one of them, the value of the exponent $\gamma$ of the distribution of the number of incoming links is between $3/2$ and $2.$ In the other scenario, $\gamma >2\mathrm{}$ and the distribution is necessarily nonstationary.