In many realistic networks, the edges representing the interactions between nodes are time varying. Evidence is growing that the complex network that models the dynamics of the human brain has time-varying interconnections, that is, the network is evolving. Based on this evidence, we construct a patient- and data-specific evolving network model (comprising discrete-time dynamical systems) in which epileptic seizures or their terminations in the brain are also determined by the nature of the time-varying interconnections between the nodes. A novel and unique feature of our methodology is that the evolving network model remembers the data from which it was conceived from, in the sense that it evolves to almost regenerate the patient data even on presenting an arbitrary initial condition to it. We illustrate a potential utility of our methodology by constructing an evolving network from clinical data that aids in identifying an approximate seizure focus; nodes in such a theoretically determined seizure focus are outgoing hubs that apparently act as spreaders of seizures. We also point out the efficacy of removal of such spreaders in limiting seizures.