Earthquake magnitude time series: Scaling behavior of visibility networks

We present a statistical analysis of earthquake magnitude sequences in terms of the visibility graph method. Magnitude time series from Italy, Southern California, and Mexico are transformed into networks and some organizational graph properties are discussed. Connectivities are characterized by a scale-free distribution with a noticeable effect for large scales due to either the presence or the lack of large events. Also, a scaling behavior is observed between different node measures like betweenness centrality, clustering coefficient, nearest neighbor connectivity, and earthquake magnitude. Moreover, parameters which quantify the difference between forward and backward links, are proposed to evaluate the asymmetry of visibility attachment mechanism. Our results show an alternating average behavior of these parameters as earthquake magnitude changes. Finally, we evaluate the effects of reducing temporal and spatial windows of observation upon visibility network properties for main-shocks.