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 $M(\cdot )$, and a star network ${g}^{\star}$ with center ${c}^{\star}$,

$\{({c}^{\star},{g}^{\star})\}\in {\mathrm{arg}max}_{(i,g)\in N\times \mathcal{G}(N)}M(i,g)$

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?

$\{({c}^{\star},{g}^{\star})\}\in {\mathrm{arg}max}_{(i,g)\in N\times \mathcal{G}(N)}M(i,g)$

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?