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rgraphnodesadjacency-matrixedges

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

Look at the imageI have a graph G and its adjacency matrix. I want to convert it into Line Graph L(G) such that nodes of graph G becomes edges in L(G) and vice-versa.
Is there any package in R which can perform such interchange from nodes to edges and edges to nodes?

Solution

  • I wrote a little function that computes the adjacency matrix of the line graph:

    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)
}

    Example:

    > 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
>