connected

1. (usually with "well-"): Having favorable rapport with a powerful entity.Examples: "Of course, he has very little money, and is rather shy in manner, but he is very well-connected."; "In human society, there is an irreconcilable conflict between the concept of financial wellbeing of the individual and the pernicious desire for increased wealth of the politically well connected."usually

2. (Canada, US) 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.Examples: "It wasn't as though there were groups of kids from mob-connected families who socialized exclusively; in fact, a consequence of growing up in a huge city like New York was that you had several groups of friends, simply due to the number and density of people."CanadaUS

3. (mathematics, topology, of a topological space) That cannot be partitioned into two nonempty open sets.Examples: "As a combinatorial subject, the connected dominating set has been studied in as early as 1970s."

4. (mathematics, graph theory, of a graph) Having a path, either directed or undirected, connecting every pair of vertices.Examples: "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."