© 2024The term resilience has become a relevant research topic in last years due to the interest of being applied to different fields and to many types of complex networks. A recently published paper proposed a theoretical and mathematical framework for a concept of local and discrete resilience, from a system performance recovery point of view. This paper deepens on this definition and provides bounds and exact values for the local resilience of some classes of networks. In addition, a new measure is defined, the composed resilience, which allows to study and compare networks from a general point of view. Several computational experiments are presented for this new parameter in different types of synthetic and real networks, providing a general measure for the resilience in complex networks.