Power-law accelerating growth complex networks with mixed attachment mechanisms

In this paper, motivated by the thoughts and methods of the mixture of preferential and uniform attachments, we extend the Barabási–Albert (BA) model, and establish a network model with the power-law accelerating growth and the mixture of the two attachment mechanisms. In our model, the number of edges generated by each newly-introduced node is proportional to the power of θ ( 0 ≤ θ < 1 ) of time t , i.e.,  m t θ . By virtue of the continuum approach, we have deduced the degree distribution P ( k , t ) of our model with the extended power-law form P ( k , t ) = A ( t ) [ k + B ( t ) ] − γ . When the number of edges k generated by each new node is much greater than the value of B ( t ) , the degree distribution P ( k , t ) will converge to the power-law form P ( k , t ) = A ( t ) k − γ . When k is much less than the value of B ( t ) , the degree distribution P ( k , t ) will converge to the exponential-law form P ( k , t ) = A ( t ) [ B ( t ) ] γ e − γ k / B ( t ) . By virtue of numerical simulations, we also discuss the dependence of the degree distribution P ( k , t ) on the model’s parameters (where t is considered as a constant in the simulations). Finally, we investigate the possible application of our model in the spreading and evolution of epidemics in some real-world systems.