Dic: connected

■ [ADJ] If one thing is connected with another, there is a link or relationship between them.

• Have you ever had any skin problems connected with exposure to the sun?... 
• The dispute is not directly connected to the negotiations...

well connected: having important or powerful friends or relatives

.... Cobuild, LDOCE

■

1. Joined or fastened together.
2. Mathematics: a. Not decomposable into two disjoint nonempty open sets.
   b. Having a continuous path between any two points. Used of a curve, set, or surface.
3. Related by family.
4. Logically or intelligibly ordered or presented; coherent: a stroke that left him incapable of connected speech.
5. Associated with or related to others, especially to influential or important people: a photographer who was well connected in the fashion world.

.... The American Heritage