# REGE - Algorithms for compiting (dis)similarities in terms of regular equivalnece REGE - Algorithms for compiting (dis)similarities in terms of regular equivalnece (White & Reitz, 1983). `REGE, REGE.for` - Classical REGE or REGGE, as also implemented in Ucinet. Similarities in terms of regular equivalence are computed. The `REGE.for` is a wrapper for calling the FORTRAN subrutine written by White (1985a), modified to be called by R. The `REGE` does the same, however it is written in R. The functions with and without ".for" differ only in whether they are implemented in R of FORTRAN. Needless to say, the functions implemented in FORTRAN are much faster. `REGE.ow, REGE.ow.for` - The above function, modified so that a best match is searched for each arc separately (and not for both arcs, if they exist, together). `REGE.nm.for` - REGE or REGGE, modified to use row and column normalized matrices instead of the original matrix. `REGE.ownm.for` - The above function, modified so that a best match for an outgoing ties is searched on row-normalized network and for incoming ties on column-normalized network. `REGD.for` - REGD or REGDI, a dissimilarity version of the classical REGE or REGGE. Dissimilarities in terms of regular equivalence are computed. The `REGD.for` is a wrapper for calling the FORTRAN subroutine written by White (1985b), modified to be called by R. `REGE.FC` - Actually an earlier version of REGE. The difference is in the denominator. See Žiberna (2007) for details. `REGE.FC.ow` - The above function, modified so that a best match is searched for each arc separately (and not for both arcs, if they exist, together). other - still in testing stage. UTF-8 ```r REGE.FC( M, E = 1, iter = 3, until.change = TRUE, use.diag = TRUE, normE = FALSE ) REGE.FC.ow( M, E = 1, iter = 3, until.change = TRUE, use.diag = TRUE, normE = FALSE ) REGE(M, E = 1, iter = 3, until.change = TRUE, use.diag = TRUE) REGE.ow(M, E = 1, iter = 3, until.change = TRUE, use.diag = TRUE) REGE.for(M, iter = 3, E = 1) REGD.for(M, iter = 3, E = 0) REGE.ow.for(M, iter = 3, E = 1) REGD.ow.for(M, iter = 3, E = 0) REGE.ownm.for(M, iter = 3, E = 1) REGE.ownm.diag.for(M, iter = 3, E = 1) REGE.nm.for(M, iter = 3, E = 1) REGE.nm.diag.for(M, iter = 3, E = 1) REGE.ne.for(M, iter = 3, E = 1) REGE.ow.ne.for(M, iter = 3, E = 1) REGE.ownm.ne.for(M, iter = 3, E = 1) REGE.nm.ne.for(M, iter = 3, E = 1) REGD.ne.for(M, iter = 3, E = 0) REGD.ow.ne.for(M, iter = 3, E = 0) ``` ## Arguments - `M`: Matrix or a 3 dimensional array representing the network. The third dimension allows for several relations to be analyzed. - `E`: Initial (dis)similarity in terms of regular equivalnece. - `iter`: The desired number of iterations. - `until.change`: Should the iterations be stopped when no change occurs. - `use.diag`: Should the diagonal be used. If `FALSE`, all diagonal elements are set to 0. - `normE`: Should the equivalence matrix be normalized after each iteration. ## Returns - **E**: A matrix of (dis)similarities in terms of regular equivalnece. - **Eall**: An array of (dis)similarity matrices in terms of regular equivalence, each third dimension represets one iteration. For ".for" functions, only the initial and the final (dis)similarities are returned. - **M**: Matrix or a 3 dimensional array representing the network used in the call. - **iter**: The desired number of iterations. - **use.diag**: Should the diagonal be used - for functions implemented in R only. ... ## Examples ```r n <- 20 net <- matrix(NA, ncol = n, nrow = n) clu <- rep(1:2, times = c(5, 15)) tclu <- table(clu) net[clu == 1, clu == 1] <- 0 net[clu == 1, clu == 2] <- rnorm(n = tclu[1] * tclu[2], mean = 4, sd = 1) * sample(c(0, 1), size = tclu[1] * tclu[2], replace = TRUE, prob = c(3/5, 2/5)) net[clu == 2, clu == 1] <- 0 net[clu == 2, clu == 2] <- 0 D <- REGE.for(M = net)$E # Any other REGE function can be used plot.mat(net, clu = cutree(hclust(d = as.dist(1 - D), method = "ward.D"), k = 2)) # REGE returns similarities, which have to be converted to # disimilarities res <- optRandomParC(M = net, k = 2, rep = 10, approaches = "hom", homFun = "ss", blocks = "reg") plot(res) # Hopefully we get the original partition ``` ## References (2008). Direct and indirect approaches to blockmodeling of valued networks in terms of regular equivalence. Journal of Mathematical Sociology, 32(1), 57-84. doi: 10.1080/00222500701790207 White, D. R., & Reitz, K. P. (1983). Graph and semigroup homomorphisms on networks of relations. Social Networks, 5(2), 193-234. White, D. R.(1985a). DOUG WHITE'S REGULAR EQUIVALENCE PROGRAM. Retrieved from http://eclectic.ss.uci.edu/~drwhite/REGGE/REGGE.FOR White, D. R. (1985b). DOUG WHITE'S REGULAR DISTANCES PROGRAM. Retrieved from http://eclectic.ss.uci.edu/~drwhite/REGGE/REGDI.FOR White, D. R. (2005). REGGE. Retrieved from http://eclectic.ss.uci.edu/~drwhite/REGGE/ #' @author based on Douglas R. White's original REGE and REGD ## See Also `sedist`, `critFunC`, `optParC`, `plot.mat`