We investigate the dynamical behavior of aftershocks in earthquake networks, and the earthquake network calculated from a time series is constructed by contemplating cell resolution and temporal causality. We attempt to connect an earthquake network using relationship between one main earthquake and its aftershocks from seismic data of California. We mainly examine some topological properties of the earthquake such as the degree distribution, the characteristic path length, the clustering coefficient, and the global efficiency. Our result cannot presently determine the universal scaling exponents in statistical quantities, but the topological properties may be inferred to advance and improve by implementing the method and its technique of networks. Particularly, it may be dealt with a network issue of convenience and of importance in the case how large networks construct in time to proceed on earthquake systems.