find_ql function

Convert index into group pair

This function is the inverse of the conversion ${(q,l), q,l}$ into ${1,...,Q^2}$ for the directed case ${(q,l), q<= l}$ into ${1,...,Q*(Q+1)/2}$ for the undirected case. It takes the integer index corresponding to $(q,l)$ and returns $(q,l)$.

find_ql(ind_ql, Q, directed = TRUE)

Arguments

• ind_ql: Converted $(q,l)$ index
• Q: Total number of groups $Q$
• directed: Boolean for directed (TRUE) or undirected (FALSE) case

Returns

Group pair $(q,l)$ corresponding to the given index

Examples

# Convert the index 5 into a group pair for undirected graph
# and the index 8 into a group pair for directed graph
# where the total number of group is 3

ind_ql_dir <- 8
ind_ql_undir <- 5

Q <- 3

directedIndex <- find_ql(ind_ql_dir,Q)
undirectedIndex <- find_ql(ind_ql_undir,Q, FALSE)