  We study the dynamics of the Olami-Feder-Christensen (OFC) model of
earthquakes, focusing on the behavior of sequences of epicenters regarded as a
growing complex network. Besides making a detailed and quantitative study of
the effects of the borders (the occurrence of epicenters is dominated by a
strong border effect which does not scale with system size), we examine the
degree distribution and the degree correlation of the graph. We detect sharp
differences between the conservative and nonconservative regimes of the model.
Removing border effects, the conservative regime exhibits a Poisson-like degree
statistics and is uncorrelated, while the nonconservative has a broad
power-law-like distribution of degrees (if the smallest events are ignored),
which reproduces the observed behavior of real earthquakes. In this regime the
graph has also a unusually strong degree correlation among the vertices with
higher degree, which is the result of the existence of temporary attractors for
the dynamics: as the system evolves, the epicenters concentrate increasingly on
fewer sites, exhibiting strong synchronization, but eventually spread again
over the lattice after a series of sufficiently large earthquakes. We propose
an analytical description of the dynamics of this growing network, considering
a Markov process network with hidden variables, which is able to account for
the mentioned properties.
