Distribution of epicenters in the Olami-Feder-Christensen model

We show that the well established Olami-Feder-Christensen (OFC) model for the dynamics of earthquakes is able to reproduce a striking property of real earthquake data. Recently, it has been pointed out by Abe and Suzuki that the epicenters of earthquakes could be connected in order to generate a graph, with properties of a scale-free network of the Barabási-Albert type. However, only the nonconservative version of the Olami-Feder-Christensen model is able to reproduce this behavior. The conservative version, instead, behaves like a random graph. Besides indicating the robustness of the model to describe earthquake dynamics, those findings reinforce that conservative and nonconservative versions of the OFC model are qualitatively different. Also, we propose a completely different dynamical mechanism that, even without an explicit rule of preferential attachment, generates a scale-free network. The preferential attachment is in this case a "byproduct" of the long term correlations associated with the self-organized critical state.