Emergence of double power-law degree distribution by controlling the evolution of BA model

Recent empirical studies have witnessed the wide existence of double power-law distribution in complex systems. However its underlying origin remains inadequately disclosed. We show this distribution can arise from the proper control of BA model. Particularly, the control policy demands each new edge to determine the range(degree <= k(c) or > k(c) of its target node by probability p before applying the preferential attachment. We analytically derive the degree distribution and demonstrate a critical control parameter p(c) so that normal and reversed double power-law degree distribution emerges for p > p(c) and p < p(c) respectively, and a single power law is recovered when p = p(c). The control policy of our model can spontaneously result from various constraints, which provides possible explanation for some real systems and indicates the validity of our model. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

Recent empirical studies have found the wide existence of double power-law distribution in complex systems, which can be explained by controlling the parameters of the BA model. The control parameter p(c) plays a critical role in determining the shape of the degree distribution, leading to different distributions for different values of p. This model can provide possible explanations for real systems and demonstrate its validity.