The research and use of the term resilience in various types of technological, physiological, and socioeconomic systems has become very topical in recent years since this term has been applied in different fields with different meanings and connotations. One of the most common meanings of resilience is related to a positive idea that addresses recovery from failures. This study proposes to establish a theoretical and mathematical framework for discrete resilience that allows different systems to be quantitatively compared from this point of view. Also, a definition and a local view of the concept of resilience applicable to different characteristic measures in the field of complex networks is provided. Furthermore, several computational experiments are presented on the values of this new parameter in different types of synthetic and real-world networks, supplying a new set of conceptual tools for network science research.