Graph theory
Fields of mathematics are typically concerned with special kinds of objects. Often such an object is said to be "connected" if, when it is considered as a topological space, it is a connected space. Thus, manifolds, Lie groups, and graphs are all called "connected" if they are connected as topological spaces, and their components are the topological components. Sometimes it is convenient to restate the definition of connectedness in such fields. For example, a graph is said to be "connected" if each pair of vertices in the graph is joined by a path. This definition is equivalent to the topological one, as applied to graphs, but it is easier to deal with in the context of graph theory. Graph theory also offers a context-free measure of connectedness, called the clustering coefficient.