A topological space is said to be connected if it is not the union of two disjoint nonempty open sets.
Graph theory also offers a context-free measure of connectedness, called the clustering coefficient.
Other fields of mathematics are concerned with objects that are rarely considered as topological spaces.
We might wish to call a topological space connected if each pair of points in it is joined by a path.
Properties and parameters based on the idea of connectedness often involve the word connectivity.
While terminology varies, noun forms of connectedness-related properties often include the term connectivity.
On the other hand, in fields without a formally defined notion of connectivity, the word may be used as a synonym for connectedness.