convertNodePair function

Convert node pair $(i,j)$

Convert node pair $(i,j)$ into an index

• Directed case :: * The node pair $(i,j)$ with $(i\neq j)$ is converted into the index $(i-1)*(n-1)+j-(i\<j)$
• Undirected case :: * The node pair $(i,j)$ with $(i\neq j)$ is converted into the index $(2*n-i)*(i-1)/2 +j-i$

convertNodePair(i, j, n, directed)

Arguments

• i: Node $i$ : $i\in {1, \ldots, n}$
• j: Node $j$ : $j\in {1, \ldots, n}$
• n: Total number of nodes : $i,j\in {1, \ldots, n}$
• directed: Boolean for directed (TRUE) or undirected (FALSE) case

Returns

Index corresponding to the node pair

Details

The number of possible node pairs is

• $N = n*(n-1)$ for the directed case
• $N = n*(n-1)/2$ for the undirected case

which corresponds to the cardinality of data$type.seq

Examples

# Convert the node pair (3,7) into an index, where the total number of nodes is 10,
# for directed and undirected graph

i <- 3
j <- 7
n <- 10

directedIndex <- convertNodePair(i,j,n,TRUE)
undirectedIndex <- convertNodePair(i,j,n,FALSE)