  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 and a loop, which 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
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. It is also found that the exponent
of the distribution of connectivities is characteristic for a plate under
investigation.
