I read about the limitations of centrality measures on Wikipedia. It says that centrality measures are good only for identifying top most important nodes in a social network. Their relative values can not be used to measure how much one node is more important than the other. The values of less important nodes are not indicative of anything at all. This made me thinking if the thing I am trying to do makes sense.
What I have is a graph (1K nodes), which has edges that dynamically change in time. New edges appear, old ones disappear. Changes are more or less subtle, gradual.
With centrality measures, I wanted to observe the following two things:
Follow top 10 important nodes at the moment and how their centrality is changing over time. For example, is closeness centrality growing in the social network or not.
Follow selected 20 nodes which might not be most important ones. I wanted to observe how their centralities are changing over time.
As you see, I would not compare nodes between each other but rather with themselves. Is this approach valid? Also, is it valid to use average values of centralities of all nodes or top N nodes?