  Discovery of a new scale-free law of earthquake phenomenon is reported. It is
relevant to the structural and dynamical properties of the earthquake network
proposed in a recent work [S. Abe and N. Suzuki, Europhys. Lett. 65, 581
(2004)]. The seismic data taken in southern California are mapped to an
evolving directed network. It is found that statistics of the degrees of
separation between two vertices is characterized by the Zipf-Mandelbrot
distribution. This shows how a given earthquake can influence a large number of
subsequent earthquakes and describes spatio-temporal criticality/complexity of
seismicity in a novel manner.
