Scale-free network of earthquakes

The district of Southern California and Japan are divided into small cubic cells, each of which is regarded as a vertex of a graph if earthquakes occur therein. Two successive earthquakes define an edge or a loop, which may replace the complex fault-fault interaction. In this way, the seismic data are mapped to a random graph. It is discovered that an evolving random graph associated with earthquakes behaves as a scale-free network of the Barabasi-Albert type. The distributions of connectivities in the graphs thus constructed are found to decay as a power law, showing a novel feature of earthquake as a complex critical phenomenon. This result can be interpreted in view of the facts that the frequency of earthquakes with large values of moment also decays as a power law (the Gutenberg-Richter law) and aftershocks associated with a mainshock tend to return to the locus of the mainshock, contributing to the large degree of connectivity of the vertex of the mainshock. Thus, a mainshock plays the role of a hub. It is also found that the exponent of the distribution of connectivities is characteristic for the plate under investigation.