a politically 'connected' businessman [=a businessman who has relationships with people who have political power]
In my mind, the two places 'are connected'. [=I think of the two places as being related to each other]
They 'are' somehow 'connected' to the royal family. [=they are related in some way to the royal family]
(..) of this demand. 'As police round up potential suspects... ' '..this viewer video shows officers raiding an address in Bradford. 'A man thought to be connected with a religious pressure group, dragged to a waiting van... ' If it's terrorists, they'll take her head off. For fuck's sake, man! (..)2011 TvShow: Black Mirror Title: The National Anthem Season: 1 Episode 1