WordNet sense 1 (connecting without a break; within a common boundary):

conterminous

WordNet sense 2 (having a common boundary or edge; touching):

adjacent, adjoining, abutting, neighboring

WordNet sense 3 (joined or linked together):

connected

WordNet sense 4 (very close or connected in space or time):

immediate

WordNet sense 5 (at or within a short distance in space or time or having elements near each other):

close