The ConnectedComponentsAlgorithm functions compute the connected components of an undirected graph using a DFS-based approach.

A connected component of an undirected graph is a set of vertices that are all reachable from each other.

If the connected components need to be maintained while a graph is growing the disjoint-set based approach of function IncrementalComponentsAlgorithm is faster. For ``static'' graphs this DFS-based approach is faster.

The output of the algorithm is recorded in the component property Components, which will contain numbers giving the component number assigned to each vertex.