Stars, Neighborhood Inclusion, and Network Centrality

The numerous network centrality indices proposed in the
literature have little in common but the operational quantification
of an intuition that nodes in better positions
are more central, where “position” is relative to a particular
conceptualization. We propose to discriminate
centrality indices from other indices by focusing on a minimal
requirement for “better” instead. Formally, we posit
that a centrality ranking must preserve the neighborhoodinclusion
preorder, and discuss advantages of such an
approach.