Getting connected components from a QuickGraph graph

Is this something you are looking for?

I would use use the RProvider to send the code to R and generate this and then wrap it in a dll if necessary. You can then use components, clusters, groups etc. to extract the connections.

# In R:
g1 <- graph(  edges=c( "1","1", "2", "18", "3", "3", "4", "5", "5", "24", "24", "6", "7", "6", "8", "9", "10", "9"),n=9,directed=T)
plot(g1)
comp1 <- components(g1)
comp1
groups(comp1)
cl <- clusters(g1)
lapply(seq_along(cl$csize)[cl$csize > 1], function(x) 
  V(g1)$name[cl$membership %in% x]) 

In case you decide to still stick to QuickGraph, what you are seeing in FSI is because you are defining a record type called Vertex that has one member called decimal of type decimal. This is a tad bit confusing, so initially I would suggest you stick to int and just generate the graph the following way:

let tup = [(1,1); (2, 18); (3, 3); (4, 5); (5, 24); (24, 6); (7, 6); (8, 9); (10, 9)]
let edges =
    tup |> List.map (fun x -> SEdge<int>(fst x, snd x))
let graph = edges.ToAdjacencyGraph()
let uniGraph = edges.ToUndirectedGraph()

You could also just write some sort of dictionary like data structure that keeps record/count of the references.

It turns out that you need to call the Compute method on the algorithm to actually get it to run!

I took your sample code and just added call to Compute:

let x = QuickGraph.Algorithms.ConnectedComponents.
          ConnectedComponentsAlgorithm(undirGraph)
x.Compute()

Once you do this, x.Components contains a dictionary that assigns an index of a component to each vertex, so if you want groups of vertices (representing components), you can just group the results by the Value (which is the component index):

x.Components 
|> Seq.groupBy (fun kv -> kv.Value)
|> Seq.map (fun (comp, vertices) -> 
    comp, vertices |> Seq.map (fun kv -> kv.Key))

This gives the following:

[ (0, [{decimal = 1M;}]); 
  (1, [{decimal = 2M;}; {decimal = 18M;}]);
  (2, [{decimal = 3M;}]);
  (3, [{decimal = 4M;}; {decimal = 5M;}; {decimal = 24M;}; 
       {decimal = 6M;}; {decimal = 7M;}]);
  (4, [{decimal = 8M;}; {decimal = 9M;}; {decimal = 10M;}]) ]