Are there any ways to understand what a centrality measure is saying (outside of the node is central) for specific measures of centrality? For example, betweenness centrality can be thought of as how important a node is for the different paths in the graph. I'm specifically looking for some idea with eigenvector centrality, since I've been having trouble understanding the applications of it.
Why should I prefer betweenness centrality over eigenvector centrality if I want some specific result, or any two measures of centrality?
For example, in almost all problems that I've read on migration networks (see here), authors choose to use betweenness centrality to describe how the breakdown of certain nodes (habitats) would impact the overall migration flow. This heuristic makes sense, you can clearly see why it would give the desired result. But sometimes they look at other measures, like weighted degree centrality. This is the part I don't understand, how do you choose which one?