connectedness in WordNet English dictionary

1. a relation between things or events (as in the case of one causing the other or sharing features with it)
   "there was a connection between eating that pickle and having that nightmare"
   connection  connexion  connectedness 
   
2. the state of being connected
   "the connection between church and state is inescapable"
   connection  link  connectedness 
   

connectedness in English Wiktionary