ConnectedGraphComponents

ConnectedGraphComponents[g] gives the connected components of the graph g.

ConnectedGraphComponents[g, {v1, v2, ...}] gives the connected components that include at least one of the vertices v1, v2, ....

ConnectedGraphComponents[g, patt] gives the connected components that include a vertex that matches the pattern patt.

ConnectedGraphComponents[{v -> w, ...}, ...] uses rules v -> w to specify the graph g.

Examples

Get connected components as subgraphs:

g = Graph[{1 <-> 2, 2 <-> 3, 4 <-> 5}];
ConnectedGraphComponents[g]

Components containing specific vertices:

ConnectedGraphComponents[g, {1}]

Please visit the official Wolfram Language Reference for more details.