1) Adjacency 2) Blood relationship 3) Close relationship 4) Closeness 5) Contact 6) Contiguity 7) Convenience 8) Distance 9) Imminence 10) Neighborhood 11) Propinquity 12) Proximity 13) Vicinage 14) Vicinity 15) Warmth 1) Adjacency 2) Contiguity 3) Contiguousness 4) Imminence 5) Propinquity 6) Proximity 
• (n.) The state or quality of being near; -- used in the various senses of the adjective. • (n.) The state or quality of being near; -- used in the various senses of the adjective.
Near'ness noun The state or quality of being near; -- used in the various senses of the adjective. 
[n] - the spatial property resulting from a relatively small distance
closeness noun the spatial property resulting from a relatively small distance; `the sudden closeness of the dock sent him into action`