Centrality without Indices: Partial Rankings and Rank Probabilities in Networks

We present an alternative approach to assess centrality in networks which does not rely on traditional indices. The work is based on neighborhood-inclusion, a partial ranking inducing relation of nodes, which was shown to be preserved by many existing centrality indices. As such, it can serve as the shared basis for centrality in networks. We argue that evaluating this partial ranking by itself allows for a generic assessment of centrality, avoiding several pitfalls that can arise when indices are applied. Additionally, we illustrate how to derive further partial rankings and introduce some probabilistic methods to, among others, compute expected centrality ranks of nodes.