Despite there being relatively frequent discourse regarding the usage and effectiveness of various node centralities when analysing the influential spreaders of a graph, I have thus far struggled to find any formal treatments of such discussions. For example, betweeness centrality is theoretically well-defined and is popular in practice for finding influential spreading members, but is there any proof of its effectiveness in this capacity (e.g. compared to any other centrality)? All the arguments I have witnessed thus far have been largely simulation/virtual-experiment based. My question is: is there anywhere I can more formal treatments of this subject matter?
Whilst I am generally curious to see if possible formal discussions around graph analysis efficacy could exist, I have my suspicions as to why this is not already the case given that formal comparisons of this nature could be infeasible... but perhaps this is not true?