In a world that's increasingly connected, many crises are related to propagation phenomena where we need to either repress the spreading (e.g. epidemics, computer viruses, fake news...) or try to accelerate it (e.g. the diffusion of a new anti-virus patch). A good understanding of such phenomena involves a knowledge of both the structure of the whole system and the specifics of the transmission process. The standard way to deal with the former has been through a characterization of the structure by the use of networks, where nodes are the components of the system where the propagation occurs, and links exist between them if there's a possibility of transmission from one component to the other. This allows to identify the super-spreaders (i.e. components that diffuse in a disproportionally large amount) as nodes with certain particular network properties. Here we propose the use of pretopology as a framework to characterize the structure of a system, as well as a new pretopological metric for the identification of super-spreaders. Since the metric can easily be transformed into an equivalent network metric, it is easy to compare its performance with some of the classical network indices of node importance. The relevance of the metric is tested by the use of some standard agent-based models of epidemics and opinion dynamics. Finally, a pretopological model of opinion diffusion is also proposed and studied
