...se equations imply for large t that [20,21] ⎧ ⎪⎨ µt , 0 ≤ γ ≤ 1 , Mγ(t) = ⎪⎩ tγ , γ > 1 , (6) where µ is a function of γ, such that, in cases of homogeneous kernels with uniform, unit amplitudes, µ ∈ =-=[1, 2]-=- for all γ ≥ 0 (µ = 1 for γ > 1), and ⎧ ( 1−γ 1 ) 1−γ (ln t) µ 1 1−γ , 0 ≤ γ < 1 , ⎪⎨ kmax(γ; t) = ⎪⎩ t , γ > 1 , s(ν) t 1 ν−1 , γ = 1 , (7) with ν ≥ 2, s being dependent on ν as well as on the manner...

...a randomly selected preexisting node to which a new one will be connected [2–4]. This simple self-organization mechanism allows one to recover the complex topological structure of scale-free networks =-=[1,3]-=-. However, in many real network systems, links perform some specific functions, and the underlying binary networks can only be considered as skeletons determining topological properties of these syste...

...ze of documents sent from this node to others. Numerical simulations of networks with degree-driven topologies indicate that the total weight distribution can display in such systems a power-law form =-=[18,19]-=-. In turn, models whose topologies are entirely controlled by weights provide a representation of real systems in which a change of network traffic due to connecting a new node to an old node strongly...

...hanism that a new node is linked to a randomly chosen preexisting node with the probability depending on the degree of the earlier node is revised. In general, this probability is assumed in the form =-=[4,20]-=- Πγ(k) = Aγ(k)/Mγ(t) (1) with the connection kernel ⎧ ⎪⎨ k Aγ(k) = ⎪⎩ γ , γ = 1 , akk , γ = 1 , (2) and with the normalization factor 1/Mγ(t) determined by Mγ(t) = kmax ∑ j=1 Aγ(j) Nj(γ; t) , (3) whe...