如何限制 igraph/R 中最短路徑的數量

Question

使用shortest.paths function 我們從圖中得到最短路徑。 現在，我想限制最短路徑的長度。

例如，當我運行下面的代碼時，我得到了從頂點到任何頂點的所有最短路徑。

df <- read.csv("~/data.csv")
g1 <- df
graph1 <- graph_from_data_frame(g1, directed = FALSE)
plot(graph1, vertex.label = V(graph1)$name)
mat <- shortest.paths(graph1)

我得到的 output

       ID_1 ID_2 ID_3 ID_4 ID_8 ID_5 ID_7 ID_100
ID_1      0    1    1    1  Inf    2    2    Inf
ID_2      1    0    2    1  Inf    1    2    Inf
ID_3      1    2    0    2  Inf    3    1    Inf
ID_4      1    1    2    0  Inf    2    1    Inf
ID_8    Inf  Inf  Inf  Inf    0  Inf  Inf      1
ID_5      2    1    3    2  Inf    0    3    Inf
ID_7      2    2    1    1  Inf    3    0    Inf
ID_100  Inf  Inf  Inf  Inf    1  Inf  Inf      0

但是，我只想保留（比如說）路徑長度為 3 ，另一個為0 or Inf 。 實際上，我不需要其他（路徑長度=3）。

此外，我想要sum of the path weight而不僅僅是路徑的數量。 我以為我可以通過只改變一行來做到這一點

mat <- shortest.paths(graph1, weights=E(graph1)$weight)

但是，如何限制路徑長度呢？

可重現的數據

structure(list(nodeA = structure(c(1L, 1L, 1L, 2L, 2L, 3L, 4L, 
5L), .Label = c("ID_1", "ID_2", "ID_3", "ID_4", "ID_8"), class = "factor"), 
    nodeB = structure(c(2L, 3L, 4L, 5L, 4L, 6L, 6L, 1L), .Label = c("ID_100", 
    "ID_2", "ID_3", "ID_4", "ID_5", "ID_7"), class = "factor"), 
    weight = c(0.5, 0.77, 0.5, 0.9, 0.44, 0.32, 0.45, 0.543)), class = "data.frame", row.names = c(NA, 
-8L))

Answer 1

對您提供的數據運行shortest.path會直接返回所有節點組合的最短路徑（路徑權重的最小總和）。

g1 <- structure(list(nodeA = structure(c(1L, 1L, 1L, 2L, 2L, 3L, 4L, 
                                         5L), .Label = c("ID_1", "ID_2", "ID_3", "ID_4", "ID_8"), class = "factor"), 
                     nodeB = structure(c(2L, 3L, 4L, 5L, 4L, 6L, 6L, 1L), .Label = c("ID_100", 
                                                                                     "ID_2", "ID_3", "ID_4", "ID_5", "ID_7"), class = "factor"), 
                     weight = c(0.5, 0.77, 0.5, 0.9, 0.44, 0.32, 0.45, 0.543)), class = "data.frame", row.names = c(NA, 
                                                                                                                    -8L))
library(igraph)

graph1 <- graph_from_data_frame(g1, directed = FALSE)
plot(graph1, vertex.label = V(graph1)$name)

mat <- shortest.paths(graph1)
mat
#>        ID_1 ID_2 ID_3 ID_4  ID_8 ID_5 ID_7 ID_100
#> ID_1   0.00 0.50 0.77 0.50   Inf 1.40 0.95    Inf
#> ID_2   0.50 0.00 1.21 0.44   Inf 0.90 0.89    Inf
#> ID_3   0.77 1.21 0.00 0.77   Inf 2.11 0.32    Inf
#> ID_4   0.50 0.44 0.77 0.00   Inf 1.34 0.45    Inf
#> ID_8    Inf  Inf  Inf  Inf 0.000  Inf  Inf  0.543
#> ID_5   1.40 0.90 2.11 1.34   Inf 0.00 1.79    Inf
#> ID_7   0.95 0.89 0.32 0.45   Inf 1.79 0.00    Inf
#> ID_100  Inf  Inf  Inf  Inf 0.543  Inf  Inf  0.000

library(reshape)

edges <- melt(mat)
edges[as.character(edges$X1)>as.character(edges$X2)&!is.infinite(edges$value),]
     X1     X2 value
2  ID_2   ID_1 0.500
3  ID_3   ID_1 0.770
4  ID_4   ID_1 0.500
6  ID_5   ID_1 1.400
7  ID_7   ID_1 0.950
11 ID_3   ID_2 1.210
12 ID_4   ID_2 0.440
14 ID_5   ID_2 0.900
15 ID_7   ID_2 0.890
20 ID_4   ID_3 0.770
22 ID_5   ID_3 2.110
23 ID_7   ID_3 0.320
30 ID_5   ID_4 1.340
31 ID_7   ID_4 0.450
47 ID_7   ID_5 1.790
61 ID_8 ID_100 0.543