connected

adjective7

1. •
   Having or supporting connections, especially when through technology such as networking software or a transportation network.
2. •
   Having favorable rapport with a powerful entity.

   • Of course, he has very little money, and is rather shy in manner, but he is very well-connected. — 2002
3. •
   Having relationships; involved with others.

   • By his father's side Mr Trumbull was connected with one of the most honorable and conspicuous families of his native state. — 1833
4. •
   (US, Canada) Involved with organized crime, specifically someone not (yet) working for a crime organization, but referred to as a "friend" by made guys/wise guys inside the organization.
5. •
   Intimate; having bonds of affection.

   • We were sitting on his bed and I was doing a lot of mirroring and chatting and just having a very connected conversation. — 2009
6. •
   That cannot be partitioned into two nonempty open sets.

   • As a combinatorial subject, the connected dominating set has been studied in as early as 1970s. — 2012
7. •
   Having a path, either directed or undirected, connecting every pair of vertices.

   • In a connected graph, there is no section (proper subset that includes all edges from each vertex in said subset) of the graph that is isolated from the rest.