The level of energy losses and the water leaks which are present in Water Distribution Networks (WDN) cause a pressure distribution pressure that affect somehow the delivery of an optimal service. When the pressure level of the WDN is more uniform from the hydraulic point of view, the reliability degree of the WDN is being increased, because the conservation of energy is maximized. The internal losses of pressure diminish the reliability of the WDN. The increase in the losses during the failure conditions can be known if the available power by unit of weight to be dissipated by the WDN exceeds the one that really is dissipated by the same WDN under normal conditions. Based on this premise Enzo Todini (2000) defined the Resilience Index as the relation between the power by unit of weight dissipated by the WDN and the power by unit of weight available to dissipate. The first term corresponds to the spent one by the configuration of pipes in friction form to give to the service and consumed in each node of the WDN in form of pressure and demand. The second term is the power given to the system by the reservoir and/or the pump. This behavior index is the tool that prioritizes the replacement of the pipes in the WDN.