Topology of growing networks accelerated by intermediary process

We examined the effect of accelerated growth (increase in the mean vertex degree) caused by internal links between pre-existing nodes on the topology of growing networks and showed that a kind of local rule, edge additions stimulated by randomly chosen intermediaries (intermediary process), not only guarantees a highly clustered structure but also induces the scale-free property on growing networks without an explicit preferential rule with the aid of accelerating growth. We relate the power-law exponent γ describing the degree distribution to the rate of acceleration and an internal factor which expresses the contribution of internal links to the rate of increase in degrees. The behavior of the internal factor generates different forms of time dependence of degrees according to whether γ>2 or γ<2. Accelerating growth plays a dominant role in the structural formation of networks based on local rules, in contrast to cases when non-local rules are applied, because similar studies showed that a simple preferential linking rule (a non-local rule) easily induces power laws without accelerating growth.