nonconnected

Nonconnected is an adjective meaning not connected; in mathematical contexts, it is often used interchangeably with disconnected, though disconnected is the standard term. It describes objects that fail to form a single connected piece.

In topology, a subset or space X is nonconnected if it can be partitioned into two nonempty disjoint open sets U and V such that X = U ∪ V. Equivalently, X contains a separation, or X can be written as a union of two nonempty disjoint open sets. A space that is not connected is said to be disconnected; if every pair of nonempty open sets intersects, the space is connected. A stronger notion is totally disconnected, where the connected components are single points.

In graph theory, a graph is nonconnected (also called disconnected) when it has more than one connected component; there is no path between vertices in different components. Examples include a graph consisting of two disjoint cycles or several isolated vertices. The number of connected components is a basic invariant.

In other fields, nonconnected may describe networks or systems lacking full interconnection; the term disconnected is more common in everyday usage.

See also: connected, disconnected, connected components, separation, totally disconnected.