The topology of an accelerated growth network

We present and investigate a general nonlinear growth network model which incorporates accelerated growth of nodes and edges, where the growth rates of edges and nodes are all time-dependent power-law functions. The acceleration of edges determines the proportion of the internal edges to the external edges, which play a key role influencing the structure of the network. On the other hand, the effects of the acceleration of nodes on the topology of the network are discussed in the present work. This model predicts an observable two-regime scale-free degree distribution, where the scaling exponents are γ1 < 2 and γ2 ≈ 3, respectively. The crossover point kcross of the degree distribution is adjusted by the growth rates of nodes and edges. The nontrivial clustering coefficient and degree assortativity coefficient are relevant to the acceleration of nodes and edges.