如何将图形转换为 R 中的等效线图/边图/交换图？

Question

我有一个图 G 及其邻接矩阵。我想将它转换为折线图 L(G)，以便图 G 的节点成为 L(G) 中的边，反之亦然。
R 中是否有任何包可以执行从节点到边缘和边缘到节点的这种交换？

Answer 1

我写了一个小函数来计算折线图的邻接矩阵：

LineGraph <- function(A)      # A: adjacency matrix
{
  n <- nrow(A)
  m <- sum(A)/2               # m: number of edges

  X <- lower.tri(A)*A         # X: still the adjacency matrix,
  X[which(X!=0)] <- 1:m       #    but edges are numbered

  p <- which(X!=0)-1
  edgeNames <- apply(matrix(c((p %% n)+1,p %/% n+1),m),1,
                     function(v){paste(sort(v),collapse=".")})      # names of the edges

  X <- X + upper.tri(X)*t(X)

  A.line <- matrix(0,m,m)     # A.line will become the adjacency matrix of the line graph
  rownames(A.line) <- edgeNames
  colnames(A.line) <- edgeNames

  apply(X,1,
        function(x)
        {
          p <- which(x!=0)
          q <- outer(x[p],m*(x[p]-1),"+")
          A.line[c(q)] <<- 1        
        } )

  A.line[(1:m)+m*(0:(m-1))] <- 0

  return(A.line)
}

示例：

> A <- matrix( c(0,1,1,1,0,
+                1,0,0,0,1,
+                1,0,0,1,0,
+                1,0,1,0,1,
+                0,1,0,1,0), 5, 5 )
> LineGraph(A)
    1.2 1.3 1.4 2.5 3.4 4.5
1.2   0   1   1   1   0   0
1.3   1   0   1   0   1   0
1.4   1   1   0   0   1   1
2.5   1   0   0   0   0   1
3.4   0   1   1   0   0   1
4.5   0   0   1   1   1   0
>

Answer 2

igraph 包中的

make_line_graph 将图形转换为其对应的折线图。

所以使用上面的邻接矩阵

library(igraph)
m <- make_line_graph(graph_from_adjacency_matrix(A, mode="undirected"))

as_adjacency_matrix(m, sparse=FALSE)
#     [,1] [,2] [,3] [,4] [,5] [,6]
#[1,]    0    1    1    1    0    0
#[2,]    1    0    1    0    1    0
#[3,]    1    1    0    0    1    1
#[4,]    1    0    0    0    0    1
#[5,]    0    1    1    0    0    1
#[6,]    0    0    1    1    1    0

如何将图形转换为 R 中的等效线图/边图/交换图？

How to convert graph to its equivalent Line Graph/ Edge Graph/ Interchange graph in R?

r

graph

nodes

adjacency-matrix

edges