WordNet sense 1 (a connecting shape):

connection, link

WordNet sense 2 (a relation between things or events (as in the case of one causing the other or sharing features with it)):

connectedness

WordNet sense 3 (the process of bringing ideas or events together in memory or imagination):

association

WordNet sense 4 (an instrumentality that connects):

connecter, connective, connector

WordNet sense 5 (the act of bringing two things into contact (especially for communication)):

joining