如何获取图中叶节点之间的所有可能路径？

Question

我想获得图表中的“连接组”列表。这是一个例子：

library(igraph)
G <- graph(c(1,2,2,3,2,5,4,5,5,6,4,7,4,8,7,8,8,9), directed=F)
plot(G)

我想获取两个叶节点之间所有可能的路径：

[1] 1 2 3
[2] 1 2 5 6
[3] 1 2 5 4 8 9
[4] 1 2 5 4 7 8 9
[5] 3 2 5 6
[6] 3 2 5 4 8 9
[7] 3 2 5 4 7 8 9
[8] 6 5 4 7 8 9
[9] 6 5 4 8 9

我正在使用 R。感谢您的帮助。

Answer 1

我不太确定这里的确切逻辑是什么，但您似乎想要获取从每个叶节点到所有其他叶节点的路径。我们可以写一个辅助函数来做到这一点。

get_leaf_paths <- function(G) {
  leafs <- V(G)[degree(G)==1]
  do.call("c", lapply(1:(length(leafs)-1), function(i) {
    all_simple_paths(G,leafs[[i]], leafs[[-(1:i)]])
  }))  
}

基本上，我们通过查找仅连接到一个其他节点的那些节点来找到叶节点，然后我们为这些节点中的每一个调用 all_simple_paths 以获得与所有其他叶节点的连接。我们只寻找与列表更靠后的其他人的联系，以避免重复。最后，我们将所有最短路径调用的结果合并到一个对象中，该对象将收集所有路径。输出看起来像这样

get_leaf_paths(G)
# [[1]]
# + 3/9 vertices, from 6d0bb8d:
# [1] 1 2 3
# [[2]]
# + 7/9 vertices, from 6d0bb8d:
# [1] 1 2 5 4 7 8 9
# [[3]]
# + 6/9 vertices, from 6d0bb8d:
# [1] 1 2 5 4 8 9
# [[4]]
# + 4/9 vertices, from 6d0bb8d:
# [1] 1 2 5 6
# [[5]]
+ 7/9 vertices, from 6d0bb8d:
# [1] 3 2 5 4 7 8 9
# [[6]]
# + 6/9 vertices, from 6d0bb8d:
# [1] 3 2 5 4 8 9
# [[7]]
# + 4/9 vertices, from 6d0bb8d:
# [1] 3 2 5 6
# [[8]]
# + 6/9 vertices, from 6d0bb8d:
# [1] 6 5 4 7 8 9
# [[9]]
# + 5/9 vertices, from 6d0bb8d:
# [1] 6 5 4 8 9

Answer 2

或许我们可以按照以下步骤操作：

根据 degree
使用combn
为每对叶子

all_simple-paths

你可以试试这个

unlist(
  combn(
    V(G)[degree(G) == 1],
    2,
    function(x) all_simple_paths(G, x[1], x[2]),
    simplify = FALSE
  ),
  recursive = FALSE
)

这给出了

[[1]]
+ 3/9 vertices, from 27e9df3:
[1] 1 2 3

[[2]]
+ 4/9 vertices, from 27e9df3:
[1] 1 2 5 6

[[3]]
+ 7/9 vertices, from 27e9df3:
[1] 1 2 5 4 7 8 9

[[4]]
+ 6/9 vertices, from 27e9df3:
[1] 1 2 5 4 8 9

[[5]]
+ 4/9 vertices, from 27e9df3:
[1] 3 2 5 6

[[6]]
+ 7/9 vertices, from 27e9df3:
[1] 3 2 5 4 7 8 9

[[7]]
+ 6/9 vertices, from 27e9df3:
[1] 3 2 5 4 8 9

[[8]]
+ 6/9 vertices, from 27e9df3:
[1] 6 5 4 7 8 9

[[9]]
+ 5/9 vertices, from 27e9df3:
[1] 6 5 4 8 9

如何获取图中叶节点之间的所有可能路径？

How to get all possible paths between leaf nodes in a graph?

r

graph-theory

igraph