G = Graph[{{1, 2}, {1, 3}, {2, 5}, {1, 5}, {6, 7}, {6, 9}, {4, 6}}];
Select[
List @@@ EdgeList[Subgraph[G, #]] & /@ ConnectedComponents[G],
Length[#]>0 &
]
{{{4, 6}, {6, 7}, {6, 9}}, {{1, 2}, {1, 3}, {2, 5}, {1, 5}}}
If "quick" was meant as "quick at runtime", then you should better avoid Graph and use SparseArray:
componentEdges[edges_] := Module[{B},
B = Transpose[With[{m = Length[edges], n = Max[edges]},
(* this builds a sparse array directly from row pointers, column indices, and nonzero values; undocumentd *)
SparseArray @@ {Automatic, {m, n}, 0, {1, {
Range[0, 2 m, 2],
Partition[Flatten[edges], 1]
},
ConstantArray[1, 2 m]}}
]];
Select[
Table[
edges[[
Flatten[edges[[Flatten[(SparseArray[Partition[c, 1] -> 1, Length[B]].B)["NonzeroPositions"]]]],
{c, SparseArray`StronglyConnectedComponents[(# -
DiagonalMatrix[Diagonal[#]]) &[BSparseArray`StronglyConnectedComponents[B.B\[Transpose]]]B\[Transpose]]}],
Length[#] > 0 &]
];
Just for comparison, the Graph-based approach:
componentEdges0[edges_] := With[{G = Graph[edges]},
Select[
List @@@ EdgeList[Subgraph[G, #]] & /@ ConnectedComponents[G],
Length[#] > 0 &]
];
And here a usage example along with timings:
edges = Developer`ToPackedArray[List @@@ EdgeList[RandomGraph[{10000, 60000}]]];
a = componentEdges0[edges]; // RepeatedTiming // First
b = componentEdges[edges]; // RepeatedTiming // First
Sort[Sort /@ a] == Sort[Sort /@ b]
0.13
0.00980084
True