3d矩阵到2d邻接矩阵或边缘列表

Question

考虑一个3 x 3 x 3立方体，其中27个元素中的每一个都沿着面连接到其他元素。立方体形状的元件具有6个侧面，因此每个元件最多可以有6个连接（例如，3×3×3立方体中的最中心元素由6个元素限定，并且具有6个连接）。

然后，让m1，m2和m3分别成为立方体的第一层，第二层和第三层。每个元素的名称是xyz，其中x，y，z是元素的行号，列号和层号。例如，元素213位于多维数据集的第二行，第一列和第三层。此元素与其他4个元素相连：其中三个元素（113, 313, 223），一个元素位于其上方（212）。

x = 3 # nrow
y = 3 # ncol
z = 3 # nlay

# print each layer as a 2D matrix
for(k in 1:z){
  m = paste0(rep(1:x, each=x), rep(1:y, times = y), k)
  print(matrix(m, nrow=x, byrow=T))
}

     [,1]  [,2]  [,3] 
[1,] "111" "121" "131"
[2,] "211" "221" "231"
[3,] "311" "321" "331"
     [,1]  [,2]  [,3] 
[1,] "112" "122" "132"
[2,] "212" "222" "232"
[3,] "312" "322" "332"
     [,1]  [,2]  [,3] 
[1,] "113" "123" "133"
[2,] "213" "223" "233"
[3,] "313" "323" "333"

Is there an out-of-the-box function in igraph or a related package for creating either an adjacency matrix OR an edge list for a network like this? I need a solution that scales to any number of rows, columns, and layers. Python solutions are welcome.

我手动创建了2D邻接矩阵，其中行和列由下面的c(m1, m2, m3)给出：

m1 = paste0(rep(1:x, each=x), rep(1:y, times = y), 1)
m2 = paste0(rep(1:x, each=x), rep(1:y, times = y), 2)
m3 = paste0(rep(1:x, each=x), rep(1:y, times = y), 3)
c(m1, m2, m3)
 [1] "111" "121" "131" "211" "221" "231" "311" "321" "331" "112" "122" "132" "212" "222" "232" "312" "322" "332"
[19] "113" "123" "133" "213" "223" "233" "313" "323" "333"

对于这个简单的例子，邻接矩阵是稀疏的，沿对角线具有0，并且是对称的。它看起来像这样：

这里是C＆P的dput()并验证。

dput(temp)
structure(c(0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0), .Dim = c(27L, 
27L), .Dimnames = list(c("111", "121", "131", "211", "221", "231", 
"311", "321", "331", "112", "122", "132", "212", "222", "232", 
"312", "322", "332", "113", "123", "133", "213", "223", "233", 
"313", "323", "333"), c("111", "121", "131", "211", "221", "231", 
"311", "321", "331", "112", "122", "132", "212", "222", "232", 
"312", "322", "332", "113", "123", "133", "213", "223", "233", 
"313", "323", "333")))

Answer 1

当节点之间的曼哈顿距离为1时有一条边，因此您可以在R中使用dist()来创建邻接矩阵：

cube_mat = expand.grid(
    x = 1:3,
    y = 1:3,
    z = 1:3
)

m_dist = as.matrix(dist(cube_mat[, 1:3], method = "manhattan", diag = TRUE))
# Zero out any distances != 1
m_dist[m_dist != 1] = 0
rownames(m_dist) = paste0(cube_mat$x, cube_mat$y, cube_mat$z)
colnames(m_dist) = paste0(cube_mat$x, cube_mat$y, cube_mat$z)
# Plot of the adjacency matrix (looks reversed because 111 is in the bottom left):
image(m_dist)

Answer 2

如果你想使用qazxsw poi的包函数：

igraph

通常，您可以使用igraph包中的函数在边缘列表，邻接矩阵之间进行操作，还可以使用

#adj <- my.adjacency.matrix
as_edgelist(graph.adjacency(adj))

生成图形。这是默认的多维数据集：

plot.igraph

plot.igraph(graph.adjacency(adj))