A connected graph is one in which every pair of vertices are joined by a chain. A graph which is not connected is called disconnected, and breaks up into connected components.
joined or linked together
architecture: links @@What's the canonical graph theory paper
(adj.): A graph is connected if every pair of vertices is connected by some path. The Bishop graph of an 8*8 chessboard is not connected; all other pieces yield connected graphs.
A space is connected if it is not the union of a pair of disjoint nonempty open sets. Equivalently, a space is connected if the only clopen sets are the whole space and the empty set.