Scale-free network of earthquakes

The district of southern California is divided into small cubic cells. Each cell is regarded as a vertex of a random graph, when earthquakes with any values of magnitude occur therein. Successive earthquakes define an edge and a loop. Then, the seismic data are analyzed from the viewpoint of an evolving random network. It is found that the distribution of connectivities in the earthquake network thus constructed exhibits scale invariance of the Barabási-Albert type. PACS numbers: 91.30.-f, 89.75.Da, 84.35.+i, 05.65.+b 1 There is growing interest in earthquake phenomenon from the viewpoint of science of complex systems [1-4]. Though seismicity is characterized by remarkably rich phenomenology, some of the known empirical laws are rather simple. The Omori law [5] for temporal distribution of aftershocks and the Gutenberg-Richter law [6] for the relationship between frequency and magnitude are classical examples and manifest the scale-free nature of earthquake phenomenon. Recently, we have studied spatio-temporal complexity of earthquake phenomenon [7,8]. We have analyzed the waiting time distribution and the distance distribution