graph theory – proof (formal) of the centrality of the nodes

Despite the relatively frequent discussions on the use and effectiveness of the various nodes centralities when analyzing influential spreaders of a graph, I have always striven to find a formal treatment for such discussions. For example, the centrality between origins is theoretically well defined and is popular in practice for finding influential members of diffusion, but is there evidence of its effectiveness as such (for example, compared to another centrality? )? All the arguments that I have witnessed so far are largely based on virtual simulations / experiments.

Although I am generally curious to see if there may be formal discussions about the effectiveness of graph analysis, I have reason to believe that this is not already the case, given that formal comparisons of this nature might be impossible … but maybe that's not true. ?

Example papers / articles: