In a graph, a (connected) component is a maximal, connected, induced subgraph. Maximal means that there is no larger connected, induced subgraph containing the vertices of the component.

a maximal collection of pixels such that a path exists between any pair of pixels in the component

a maximal connected set of vertices

a maximal subgraph in which all nodes are reachable from every other

a set of objects such that each object is connected to at least one other member of the set and the set is maximal with respect to this property

A connected component of a space is a maximal connected subspace. The connected components of a space form a partition of that space.

In an undirected graph, a connected component or component is a maximal connected subgraph. Two vertices are in the same connected component if and only if there exists a path between them. In a drawing of a graph, the connected components can each be drawn separately with empty space between them.