The use of networks to model and study relationships between seismic events has been used in the past for small areas of the globe. Here we demonstrate that similar techniques could also be used at the global level. More importantly, many of the techniques used in complex networks analysis were used here to show that there seem to exist long-distance relations between seismic events.

First we argued in favor of the long-distance relation hypothesis by showing that the network has small-world characteristics. Given the small-world characteristics of high clustering and low average path length, we were able to argue that seisms around the world appear not to be independent of each other. To strengthen this argument, we decided to do a temporal analysis of our network. Plotting the probability distribution for the time intervals between successive earthquakes, we have found that this distribution is well fitted by a $q$-exponential, indicating a behavior described by the non-extensive statistical mechanics, which obtain $q$-exponential distributions from the generalized Tsallis entropy. This non-extensive behavior also contributes to the long-distance relation hypothesis, since the non-extensive statistical has been used to explain many complex systems with long-range interactions and long-range temporal memory.

\green{Another interesting approach we intend to do in the future relates to using community analysis or community detection to understand how seismic locations are grouped. We believe that given the long-range relations that we found here it is unlikely that the globe would be well organized around local communities of nodes (geographical locations).}