Here , we developed a complex network of solar active regions ( ARs ) to study various local and global properties of the network .
The values of the Hurst exponent ( 0.8 - 0.9 ) were evaluated by both the detrended fluctuation analysis and the rescaled range analysis applied on the time series of the AR numbers .
The findings suggest that ARs can be considered as a system of self-organized criticality .
We constructed a growing network based on locations , occurrence times , and the lifetimes of 4,227 ARs recorded from 1 January 1999 to 14 April 2017 .
The behaviour of the clustering coefficient shows that the ARs network is not a random network .
The logarithmic behaviour of the length scale has the characteristics of a so-called “ small-world network ” .
It is found that the probability distribution of the node degrees for undirected networks follows the power-law with exponents of about 3.7 to 4.2 .
This indicates the scale-free nature of the ARs network .
The scale-free and small-world properties of the ARs network confirm that the system of ARs forms a system of self-organized criticality .
Our results show that the occurrence probability of flares ( classified by GOES class C > 5 , M , and X flares ) in the position of the ARs network hubs take values greater than that obtained for other nodes .