Complex Network View of the Sun’s Magnetic Patches. I. Identification

Solar and stellar magnetic patches (i.e., magnetic fluxes that reach the surface from the interior) are believed to be the primary sources of a star’s atmospheric conditions. Here, we apply the complex network approach and investigate its efficacy in the identification of these features. For this purpose, we use the line-of-sight magnetograms provided by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. We construct the magnetic network following a specific visibility graph condition between pairs of pixels with opposite polarities and search for possible links between these regions. The complex network facilitates the construction of node degrees and PageRank images, and applying the downhill algorithm to node-degree images allows for the grouping of pixels into features corresponding to one-to-one matches with magnetogram patches. This approach promisingly serves to identify the nontrivial morphological structure of the magnetic patches for small and large sizes. We observe that the changes in the features of the node-degree images effectively correspond to the cospatial magnetic patches over time. Through visual assessment, we estimate an average false-negative error rate of approximately 1% in identifying small-scale features (one or two pixels in size).