Earthquake aftershock networks generated on Euclidean spaces of different fractal geometry

According to some recent analysis (M. Baiesi and M. Paczuski, Phys. Rev. E {\bf 69}, 066106, 2004 \cite{maya1}) of earthquake data, aftershock epicenters can be considered to represent the nodes of a network where the linking scheme depends on several factors. In the present paper a model network of earthquake aftershock epicenters is proposed based on this scheme and studied on fractals of different dimensions. The various statistical features of this network, like degree, link length, frequency and correlation distributions are evaluated and compared to the observed data. The results are also found to be independent of the fractal geometry.