In order to overcome the limitations given by transistor-based systems working in the Von Neumann architecture, it is necessary to develop new technologies and computing paradigms. In this framework, brain-inspired structures allow to perform spatio-temporal correlated operations, typical of neural circuits: in particular, the Memristor is one of the new analog devices which lets this approach possible. Defined as the fourth circuit element, the memristor is a passive element which exhibits non-linearities in its dynamics, thanks to the change in the internal resistance state due to the rearrangement of the atomic structure. Here, the computational capabilities of self-organized memristive nanowire (NW) networks are investigated by simulations: thanks to its resistive switching and fading memory properties, the system is capable of mimicking human brain's synapses basic functions in processing external signals.