 # Some have proposed that for a natural centrality measure, the most central a node can get is the cen Justine Webster 2022-05-07 Answered
Some have proposed that for a natural centrality measure, the most central a node can get is the center node in the star network. I've heard this called "star maximization." That is, for a measure $M\left(\cdot \right)$, and a star network ${g}^{\star }$ with center ${c}^{\star }$,
$\left\{\left({c}^{\star },{g}^{\star }\right)\right\}\in {\mathrm{arg}max}_{\left(i,g\right)\in N×\mathcal{G}\left(N\right)}M\left(i,g\right)$
where $N$ is the set of nodes and $\mathcal{G}$ considers all unweighted network structures.

I'd like to learn about some centrality measures that don't satisfy this property, but "star maximization" isn't a heavily used term, so I am having trouble in searching for many such measures. What are some such measures of centrality?
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A centrality measure will display star maximization under very weak conditions.
Suppose you normalize the sum of centralities to 1. Then as long as you assign zero centrality to peripheral nodes (those connected to just one other node) the centre must have the maximal centrality 1.