Eigenvector centrality comparison Let's say we calculate the eigenvector centrality of the same set of nodes in different years (we have a network each year). Note that the eigenvector centrality is normalized in such a way that the norm would be equal to one. Does it make sense to compare the measured values in different years? How can I see the dynamics of this measure in years in a fair manner? If the comparison would always be relative, what other measures can I compute? Any paper/book recommendations would also be appreciated!
 A: As often with such questions, you can do a lot of things and a lot of things have been done by other people, crucial thing is what addresses your underlying scientific question.
For example comparing (normalised) eigenvector centralities for a given node will tell you about whether the relative importance of a node changed. This may be totally relevant information for your scientific question as well as it may not be. If you consider the absolute importance to be more relevant to your scientific question, you should also need to take the change of link numbers/strengths into account (e.g., as reflected by the largest eigenvector). If you just care about what nodes are most important, you can look at the ranks of the eigenvector centralities (within a given network) instead of the absolute values.
I generally recommend to primarily think about what question a given metric answers and see whether that is useful to you as well as thinking about what question you want answered and see whether a reasonable metric straightforwardly arises from that. This does not mean that looking at the literature is not useful – it may inspire you to formulate the right metric and hint to problems that you haven’t thought about –, but if you focus only on what is frequently done or has been done before, you risk steering away from what is important to your application.
