Abstract
We study the light curves of pulsating variable stars using a complex network approach to build visibility graphs. We consider various types of variables stars (e.g., Cepheids, δ Scuti, RR Lyrae), build two types of graphs (the normal visibility graph (VG) and the horizontal visibility graph (HVG)), and calculate various metrics for the resulting networks. We find that all networks have a power-law degree distribution for the VG and an exponential distribution for the HVG, suggesting that it is a universal feature, regardless of the pulsation features. Metrics such as the average degree, the clustering coefficient and the transitivity coefficient, can distinguish between some star types. We also observe that the results are not strongly affected by the presence of observation gaps in the light curves. These findings suggest that the visibility graph algorithm may be a useful technique to study variability in stars.
Highlights
An interesting problem is how to build a complex network from a time series, which is a universal problem, considering that time series is the primary input that basic sciences receive from nature
The visibility graph (VG) is a geometrical way to build a complex network from a time series, where every data point in a 2D plot is a node, and two nodes are connected if they can be joined by a visibility line; all intermediate data lie below that line
We show the results obtained when the VG and horizontal visibility graph (HVG) techniques are applied to the light curves of the selected stars, for each of the three strategies to deal with the gaps
Summary
Several ways to build these networks have been proposed [10], but there is one which leads to interesting results, called the visibility graph algorithm [11], which takes a time series and maps it into a graph. In this graph, a node corresponds to a given datum in the time series, and two nodes are connected if visibility exists between the corresponding data, i.e. if there is a straight line that connects the data, provided that this “visibility line” is always above the data curve. This method can be used to detect nontrivial properties from the series, such as fractality [11] and reversibility [16]
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