noun, plural centralities.
a central position or state: the centrality of the sun.
a vital, critical, or important position: the centrality of education to modern civilization.

1640–50; central1 + -ity

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World English Dictionary
centrality (sɛnˈtrælɪtɪ)
n , pl -ties
the state or condition of being central

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

1640s, from central + -ity.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
The idea of the neurons' centrality to social intelligence is gaining ground.
We humans are obsessed with our centrality in the universe and that everything
  about us is special or sacred.
The second, less obvious element may well be the increased centrality to
  political decision of the po poles.
Opposing the centrality of negotiations is not a principle but a pragmatic
  reading of current reality.
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