Complex Network for Solar Active Regions

Abstract: 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 \textquotedblleft small-world network\textquotedblright. 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.