从QuickGraph图表中获取连接的组件

Question

我是图论的新手.

我已经使用QuickGraph库创建了一个邻接图,最终,我希望从图中获得连接的组件.

open QuickGraph

let tup = [(1M,1M); (2M, 18M); (3M, 3M); (4M, 5M); (5M, 24M); (24M, 6M); (7M, 6M); (8M, 9M); (10M, 9M)]

type Vertex = {decimal: decimal}

let edges = 
    tup
    |> List.map (fun x -> ({decimal = fst x}, {decimal = snd x}))
    |> List.map (fun x -> Edge<Vertex> x)

//Undirected Graph
let undirGraph = edges.ToUndirectedGraph()

undirGraph.Edges
undirGraph.Vertices

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

输出来自undirGraph.Edges:

val it : Collections.Generic.IEnumerable<Edge<Vertex>> =
seq
[FSI_0227+Vertex->FSI_0227+Vertex {Source = {decimal = 1M;};
                                       Target = {decimal = 1M;};};
 FSI_0227+Vertex->FSI_0227+Vertex {Source = {decimal = 2M;};
                                   Target = {decimal = 18M;};};
 FSI_0227+Vertex->FSI_0227+Vertex {Source = {decimal = 3M;};
                                   Target = {decimal = 3M;};};
 FSI_0227+Vertex->FSI_0227+Vertex {Source = {decimal = 4M;};
                                   Target = {decimal = 5M;};}; ...]

来自undirGraph.Vertices:

val it : Collections.Generic.IEnumerable<Vertex> =
seq
[{decimal = 1M;}; {decimal = 2M;}; {decimal = 18M;}; {decimal = 3M;}; ...]

正如所料.

无向图已成功创建,但现在我被卡住了.从这里开始,我不知道如何获取图形的连通组件,或者坦率地说,如果我使用正确的图形结构.

我原本希望x在图表中包含组件,但x;;在FSI中的输出如下所示:

该示例中的值tuple list表示BillTo与ShipTo在数据库中的客户ID的值.

QuickGraph库中的文档很少,特别是对于试图"即时学习"的人.

这个问题取代了我发布的上一个问题.我曾考虑修改我之前的问题,但由于这是一个完全独立的问题,所以决定将其保留原样.

Answer 1

这是你要找的东西吗？

我会使用RProvider将代码发送给R并生成它,然后在必要时将其包装在dll中.然后,您可以使用components,clusters,groups等提取的连接.

# 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]) 

如果您决定仍然坚持使用QuickGraph,那么您在FSI中看到的是因为您正在定义一个名为的记录类型Vertex,其中有一个名为decimal的十进制成员.这有点让人困惑,所以最初我建议你坚持下去int并按照以下方式生成图表:

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()

你也可以写一些像数据结构这样的字典来保存引用的记录/计数.

Answer 2

事实证明，您需要调用Compute算法上的方法才能使其真正运行！

我接受了您的示例代码，并添加了对Compute以下内容的调用：

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

执行此操作后，将x.Components包含一个字典，该字典为每个顶点分配一个组件的索引，因此如果您想要顶点组（代表组件），您只需按Value（这是组件索引）对结果进行分组：

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

这给出了以下内容：

[ (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;}]) ]