What is "connected component"

n. (context topology and graph theory English) A connected subset that is, moreover, maximal with respect to being connected.

In graph theory, a connected component (or just component) of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph. For example, the graph shown in the illustration on the right has three connected components. A vertex with no incident edges is itself a connected component. A graph that is itself connected has exactly one connected component, consisting of the whole graph.

Connected component may refer to:

• Connected component (graph theory), a set of vertices in a graph that are linked to each other by paths
• Connected component (topology), a maximal subset of a topological space that cannot be covered by the union of two disjoint open sets