closeness

noun6

1. •
   The state of being close (all senses).
2. •
   The state of being friends.
3. •
   The state of being secretive.
4. •
   The state of being mean or stingy.
5. •
   The shortest path between two vertices in a graph.
6. •
   (no longer used) Solitude, seclusion.

   • I thus neglecting worldly ends, all dedicated / To closeness and the bettering of my mind [...] — 1610