A connected component is a list of vertices of a graph that are connected, in other words there exists a path of edges between any two vertices in the component.
i1 : G = graph(toList(1..8),{{1,2},{2,3},{3,4},{5,6}});
i2 : connectedComponents G
o2 = {{1, 2, 3, 4}, {5, 6}, {7}, {8}}
o2 : List
See also
isConnected -- determines whether a graph is connected
numberOfComponents -- computes the number of connected components of a graph