being joined in close association.

A graph is connected if there is a path connecting every pair of vertices. A graph that is not connected can be divided into connected components (disjoint connected subgraphs). For example, this graph is made of three connected components.

Attribute of a graph or a component. A graph is called connected if it consists of exactly one component. See Also Component.

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.