在有向图中设置方向

Question

我有以下无向图g，它是从河流的shapefile中生成的。我想将g转换为有向图，其中顶点55是根，所有边缘的“方向”都朝向根顶点（想象水从网络的所有部分流向根）

无向图示例：

library(igraph)

g <- structure(list(From = c(48, 37, 39, 32, 38, 36, 49, 46, 31, 26, 
      33, 35, 18, 23, 45, 41, 42, 47, 52, 51, 50, 54, 16, 14, 8, 10, 
      5, 6, 17, 11, 20, 24, 2, 3, 1, 0, 44, 4, 7, 29, 30, 34, 40, 53, 
      43, 15, 9, 28, 27, 12, 13, 19, 21, 22, 25), To = c(32, 32, 31, 
        31, 33, 33, 45, 45, 23, 23, 26, 26, 16, 16, 35, 35, 41, 41, 50, 
        50, 47, 47, 6, 6, 5, 5, 2, 2, 10, 10, 11, 11, 1, 1, 0, 55, 30, 
        3, 3, 28, 28, 29, 29, 40, 40, 7, 7, 22, 22, 9, 9, 13, 13, 19, 
        19)), class = "data.frame", row.names = c(NA, -55L))

g <- graph.data.frame(g, directed = FALSE) 

l <- igraph::layout_as_tree(g, flip.y = FALSE)
plot(g,
    vertex.size = 10,
    vertex.color = "darkgray",
    layout = l)

我可以执行以下操作来创建有向图，但是某些边沿正确的方向定向，而其他边则不正确。

g2 <- get.adjacency(g, sparse = F)
g2[upper.tri(g2)] <- 0
g2 <- igraph::graph.adjacency(g2)

plot(g2,
      vertex.size = 10,
      vertex.color = "darkgray",
      layout = l)

我可以看到问题是由于如何标记邻接矩阵中的顶点而无法提出解决方案。

我的问题：是否可以将无向图转换为有向图，使所有边的方向都朝向选定的顶点（在本例中为顶点55）？

如果顶点被重命名等是很好的。

Answer 1

对于连接顶点a和b的每个边，如果a到55的最短距离短于b到55的最短距离，则b朝向a。我对igraph不熟悉，但是我基于以下理由提出了一种方法：

d <- distances(g)[, '55']
dd <- outer(d, d, FUN = '>')

g2 <- get.adjacency(g, sparse = F)
g2 <- g2 * dd
g2 <- igraph::graph.adjacency(g2)

plot(g2,
    vertex.size = 10,
    vertex.color = "darkgray",
    layout = l)

注意：通过将outer(d, d, FUN = '>')更改为outer(d, d, FUN = '<')，可以反转所有箭头的方向。