Centrality without Indices: Expected Ranks and Rank Probabilities in Networks

Abstract

We present an alternative approach to centrality measurement in networks which does not rely on indices. Our work is based on the concept of positional dominance, a partial ranking inducing relation of vertices, which was shown to be preserved by many centrality indices. As such, it represents the shared basis for centrality measurement. Since centrality-based node rankings can be characterized as the completions of the partial dominance ranking, it is possible to argue about all possible rankings at once. We can compute expected ranks (how central do we expect a node to be?) or, in the case where only a subset of nodes is of interest, relative rank probabilities (how likely is it that a node is more central than another?). This probabilistic approach offers a more generic and robust assessment of centrality and allows for more domain-specific reasoning. Additionally, it allows to shift the focus from probing and crafting indices to examining relevant network characteristics that make nodes central. By means of application examples, we illustrate how this approach can augment or even replace traditional index-based centrality analyses.

Date
Location
Mainz, Germany