adjective (usually with "well-"): Having favorable rapport with a powerful entity.
adjective Having relationships; involved with others.
adjective 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.
adjective Intimate; having bonds of affection.
adjective That cannot be partitioned into two nonempty open sets.
adjective 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.
adjective Having or supporting connections, especially when through technology such as networking software or a transportation network.