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R/ig_icmotif_count.R
In ILSM: Analyze Interconnection Structure of Tripartite Interaction Networks
Defines functions
ig_icmotif_count
Documented in
ig_icmotif_count
#' Count interconnection motifs for tripartite networks with intra-guild interactions
#'
#' Counting the frequencies of interconnection motifs for a tripartite interaction network with intra-guild interactions.
#'
#' @param mat A square block interaction matrix representing a tripartite network including intra-guild and inter-guild interactions. See details.
#' @param guilds A character vector matching rows of \code{mat} to indicate the guilds using ('a','b' and 'c'). See details.
#' @param weighted Logical. Default to FALSE. If TRUE, the arithmetic mean of the subgraph weights is provided for each motif. See details
#' @import igraph
#'
#' @encoding UTF-8
#'
#' @export
#'
#' @details
#' This function is designed for tripartite networks with intra-guild interactions. The input network should be nput as a block matrix (\eqn{M}) to represent three groups of nodes (a-nodes, b-nodes and c-nodes): three intra-guild interaction matrices (\eqn{m_{aa},m_{bb},m_{cc}}),
#' two inter-guild matrices of a and b-nodes (\eqn{m_{ab},m_{ba}}), and two inter-guild matrices of b- and c-nodes(\eqn{m_{bc},m_{cb}}).
#' \deqn{
#' \left(
#' \begin{array}{ccc}
#' m_{aa} & m_{ab} & 0 \\
#' m_{ba} & m_{bb} & m_{bc} \\
#' 0 & m_{cb} & m_{cc}
#' \end{array}
#' \right)
#' }
#'
#' \code{guilds} should be a vector of the same length as the row of \code{mat} like c("a","a"..."b","b"..."c","c"..)
#'
#' \strong{Interconnection motifs in tripartite networks with intra-guild interactions}
#' <br>An interconnection motif is defined to comprise three sets of connected nodes: the connector nodes (belonging to b-nodes), the nodes in one subnetwork (belonging to a-nodes in the P subnetwork), and the nodes in the other subnetwork (belonging to c-nodes in the Q subnetwork). Each guild has two nodes at most, resulting in a total of 107 distinct motif forms.
#' The algorithm for counting interconnection motifs is designed by extending the fast approach from Simmons et al.(2019). For interconnection motifs in tripartite networks without intra-guild interactions, please see **icmotif_count** and **icmotif_role**.
#'
#' \strong{Weighted networks}
#' <br>For weighted tripartite networks, the mean weight of a given motif is provided by averaging the weights of all motif occurrences isomorphic to the motif. The weight of a motif occurrence is the arithmetic mean of the weights of its links, following Mora et al. (2018) and Simmons et al. (2019).
#'
#'
#' @return
#' Return a matrix of counts (and mean weight) of 107 interconnection motifs.
#'
#'
#' @references
#' Garcia-Callejas, D., Godoy, O., Buche, L., Hurtado, M., Lanuza, J.B., Allen-Perkins, A. et al. (2023) Non-random interactions within and across guilds shape the potential to coexist in multi-trophic ecological communities. Ecology Letters, 26, 831-842.
#'
#' Pilosof, S., Porter, M. A., Pascual, M., & KC)fi, S. (2017). The multilayer nature of ecological networks. Nature Ecology & Evolution, 1(4), 0101.
#'
#' Mora, B.B., Cirtwill, A.R. and Stouffer, D.B. (2018). pymfinder: a tool for the motif analysis of binary and quantitative complex networks. bioRxiv, 364703.
#'
#' Simmons, B. I., Sweering, M. J., Schillinger, M., Dicks, L. V., Sutherland, W. J., & Di Clemente, R. (2019). bmotif: A package for motif analyses of bipartite networks. Methods in Ecology and Evolution, 10(5), 695-701.
#'
#' @examples
#'
#' ##A toy tripartite network with intra-guild negative interactions:
#' ##Inter-guild mutualistic interactions and inter-guild antagonistic interactions.
#' set.seed(12)
#' ##4 a-nodes, 5 b-nodes, and 3 c-nodes
#'
#' ##Intra-guild interaction matrices
#' mat_aa<-matrix(runif(16,-0.8,-0.2),4,4)
#' mat_aa <- mat_aa + t(mat_aa); diag(mat_aa) <- 0
#' mat_bb<-matrix(runif(25,-0.8,-0.2),5,5)
#' mat_bb <- mat_bb + t(mat_bb); diag(mat_bb) <- 0
#' mat_cc<-matrix(runif(9,-0.8,-0.2),3,3)
#' mat_cc <- mat_cc + t(mat_cc); diag(mat_cc) <- 0
#'
#' ##Inter-guild interaction matrices between a- and b-nodes.
#' mat_ab<-mat_ba<-matrix(sample(c(rep(0,8),runif(12,0,0.5))),4,5,byrow=TRUE)
#' mat_ba<-t(mat_ba)
#'
#' ##Inter-guild interaction matrices between b- and c-nodes.
#' mat_cb<-mat_bc<-matrix(sample(c(rep(0,8),runif(7,0,0.5))),3,5,byrow=TRUE)
#' mat_bc<--t(mat_bc)
#' mat<-rbind(cbind(mat_aa,mat_ab,matrix(0,4,3)),cbind(mat_ba,mat_bb,mat_bc))
#' mat<-rbind(mat,cbind(matrix(0,3,4),mat_cb,mat_cc))
#'
#' ##set the node names
#' rownames(mat)<-c(paste0("a",1:4),paste0("b",1:5),paste0("c",1:3))
#' colnames(mat)<-c(paste0("a",1:4),paste0("b",1:5),paste0("c",1:3))
#'
#' #mat[mat!=0] <- 1
#' myguilds=c(rep("a",4),rep("b",5),rep("c",3))
#' ig_icmotif_count(mat,guilds=myguilds,TRUE)
#'
#'
ig_icmotif_count <-
function(mat, guilds,weighted =FALSE) {
if (inherits(mat, c("matrix", "data.frame")) == T || ncol(mat)==nrow(mat)){
if(length(guilds)!= nrow(mat))
stop("guilds should be a vector of the same length as the row of mat!")
else{
if(sum(unique(guilds)%in%c("a","b","c"))!=3)
stop("guilds should be composed of these three characters (a,b,c)!")
else{
if(is.null(dimnames(mat)) || sum(rownames(mat)!=colnames(mat))!=0 )
stop("Make sure this matrix either have the same row and column names [No NA!!!]")
else{
mat <- abs(mat)
subnet_mat1 <- mat[guilds == "a", guilds == "b"]
subnet_mat2 <- mat[guilds == "b", guilds == "c"]
AA <- mat[guilds == "a", guilds == "a"]
BB <- mat[guilds == "b", guilds == "b"]
CC <- mat[guilds == "c", guilds == "c"]
}
}
}
}
else
stop("mat should be a square block interaction matrix!")
dimnames(subnet_mat1) <- NULL
dimnames(subnet_mat2) <- NULL
P <- subnet_mat1
Q <- subnet_mat2
PW <- P; QW <- Q; AAW <- AA; BBW <- BB; CCW <- CC
AA <- (AA!=0)*1; BB <- (BB!=0)*1; CC <- (CC!=0)*1
P <- (P!=0)*1; Q <- (Q!=0)*1
AA_no <- AA == 0
diag(AA) <- 0
diag(AA_no) <- 0
AA_two <- (AA!=0)*1
BB_no <- BB == 0
diag(BB) <- 0
diag(BB_no) <- 0
BB_two <- (BB!=0)*1
CC_no <- CC == 0
diag(CC) <- 0
diag(CC_no) <- 0
CC_two <- (CC!=0)*1
Ob <- colSums(P); Rb <- rowSums(Q)
Ubb <- t(P) %*% P
Vbb <- Q %*% t(Q)
UVbb <- Ubb * Vbb
B2C_NO <- rowSums((Q%*%CC_no) *Q) /2
B2C_YES <- rowSums((Q%*%CC_two) *Q) /2
B2A_NO <- rowSums((t(P)%*%AA_no) *t(P)) /2
B2A_YES <- rowSums((t(P)%*%AA_two) *t(P)) /2
M111 <- sum(Ob * Rb)
M112_1 <- sum(Ob * B2C_NO)
M112_2 <- sum(Ob * B2C_YES)
M211_1 <- sum(B2A_NO * Rb)
M211_2 <- sum(B2A_YES * Rb)
M212_1 <- sum(B2A_NO * B2C_NO)
M212_2 <- sum(B2A_YES * B2C_NO)
M212_3 <- sum(B2A_NO * B2C_YES)
M212_4 <- sum(B2A_YES * B2C_YES)
mat_tri <- function(mat) {sum(mat[upper.tri(mat)])}
M121_1 <- mat_tri(UVbb * BB_no)
M121_2 <- mat_tri(UVbb * BB_two)
P_all_yes <- t(apply(P, 2, function(x) { A <- x %*% t(x); A * AA}))
P_one_yes <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); A *AA}))
P_two_yes <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); t(A) *AA}))
P_all_no <- t(apply(P, 2, function(x) { A <- x %*% t(x); A * AA_no}))
P_one_no <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); A * AA_no}))
P_two_no <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); t(A) * AA_no}))
Q_all_yes <- t(apply(Q, 1, function(x) { A <- x %*% t(x); A * CC}))
Q_one_yes <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); A * CC}))
Q_two_yes <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); t(A) * CC}))
Q_all_no <- t(apply(Q, 1, function(x) { A <- x %*% t(x); A * CC_no}))
Q_one_no <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); A * CC_no}))
Q_two_no <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); t(A) * CC_no}))
AA_no_P_2 <- P_two_no %*% t(P_one_no)
AA_yes_P_2 <- P_two_yes %*% t(P_one_yes)
AA_no_P_3 <- P_all_no %*% t(P_one_no)
AA_yes_P_3 <- P_all_yes %*% t(P_one_yes)
AA_no_P_3t <- t(AA_no_P_3)
AA_yes_P_3t <- t(AA_yes_P_3)
AA_no_P_4 <- (P_all_no %*% t(P_all_no)) / 2
AA_yes_P_4 <- (P_all_yes %*% t(P_all_yes)) / 2
CC_no_Q_2 <- Q_two_no %*% t(Q_one_no)
CC_yes_Q_2 <- Q_two_yes %*% t(Q_one_yes)
CC_no_Q_3 <- Q_all_no %*% t(Q_one_no)
CC_yes_Q_3 <- Q_all_yes %*% t(Q_one_yes)
CC_no_Q_4 <- (Q_all_no %*% t(Q_all_no)) / 2
CC_yes_Q_4 <- (Q_all_yes %*% t(Q_all_yes)) / 2
M122_1_1 <- mat_tri(Ubb * BB_no * CC_no_Q_2)
M122_1_2 <- mat_tri(Ubb * BB * CC_no_Q_2)
M122_1_3 <- mat_tri(Ubb * BB_no * CC_yes_Q_2)
M122_1_4 <- mat_tri(Ubb * BB * CC_yes_Q_2)
M122_2_1 <- sum(Ubb * BB_no * CC_no_Q_3)
M122_2_2 <- sum(Ubb * BB * CC_no_Q_3)
M122_2_3 <- sum(Ubb * BB_no * CC_yes_Q_3)
M122_2_4 <- sum(Ubb * BB * CC_yes_Q_3)
M122_3_1 <- mat_tri(Ubb * BB_no * CC_no_Q_4)
M122_3_2 <- mat_tri(Ubb * BB * CC_no_Q_4)
M122_3_3 <- mat_tri(Ubb * BB_no * CC_yes_Q_4)
M122_3_4 <- mat_tri(Ubb * BB * CC_yes_Q_4)
M221_1_1 <- mat_tri(AA_no_P_2 * BB_no * Vbb)
M221_1_2 <- mat_tri(AA_yes_P_2 * BB_no * Vbb)
M221_1_3 <- mat_tri(AA_no_P_2 * BB * Vbb)
M221_1_4 <- mat_tri(AA_yes_P_2 * BB * Vbb)
M221_2_1 <- sum(AA_no_P_3 * BB_no * Vbb)
M221_2_2 <- sum(AA_yes_P_3 * BB_no * Vbb)
M221_2_3 <- sum(AA_no_P_3 * BB * Vbb)
M221_2_4 <- sum(AA_yes_P_3 * BB * Vbb)
M221_3_1 <- mat_tri(AA_no_P_4 * BB_no * Vbb)
M221_3_2 <- mat_tri(AA_yes_P_4 * BB_no * Vbb)
M221_3_3 <- mat_tri(AA_no_P_4 * BB * Vbb)
M221_3_4 <- mat_tri(AA_yes_P_4 * BB * Vbb)
M222_1_1 <- sum(AA_no_P_3 * BB_no * CC_no_Q_2)
M222_1_2 <- sum(AA_yes_P_3 * BB_no * CC_no_Q_2)
M222_1_3 <- sum(AA_no_P_3 * BB * CC_no_Q_2)
M222_1_4 <- sum(AA_no_P_3 * BB_no * CC_yes_Q_2)
M222_1_5 <- sum(AA_yes_P_3 * BB * CC_no_Q_2)
M222_1_6 <- sum(AA_yes_P_3 * BB_no * CC_yes_Q_2)
M222_1_7 <- sum(AA_no_P_3 * BB * CC_yes_Q_2)
M222_1_8 <- sum(AA_yes_P_3 * BB * CC_yes_Q_2)
M222_2_1 <- mat_tri(AA_no_P_4 * BB_no * CC_no_Q_2)
M222_2_2 <- mat_tri(AA_yes_P_4 * BB_no * CC_no_Q_2)
M222_2_3 <- mat_tri(AA_no_P_4 * BB * CC_no_Q_2)
M222_2_4 <- mat_tri(AA_no_P_4 * BB_no * CC_yes_Q_2)
M222_2_5 <- mat_tri(AA_yes_P_4 * BB * CC_no_Q_2)
M222_2_6 <- mat_tri(AA_yes_P_4 * BB_no * CC_yes_Q_2)
M222_2_7 <- mat_tri(AA_no_P_4 * BB * CC_yes_Q_2)
M222_2_8 <- mat_tri(AA_yes_P_4 * BB * CC_yes_Q_2)
M222_3_1 <- sum(AA_no_P_2 * BB_no * CC_no_Q_3)
M222_3_2 <- sum(AA_yes_P_2 * BB_no * CC_no_Q_3)
M222_3_3 <- sum(AA_no_P_2 * BB * CC_no_Q_3)
M222_3_4 <- sum(AA_no_P_2 * BB_no * CC_yes_Q_3)
M222_3_5 <- sum(AA_yes_P_2 * BB * CC_no_Q_3)
M222_3_6 <- sum(AA_yes_P_2 * BB_no * CC_yes_Q_3)
M222_3_7 <- sum(AA_no_P_2 * BB * CC_yes_Q_3)
M222_3_8 <- sum(AA_yes_P_2 * BB * CC_yes_Q_3)
M222_4_1 <- sum(AA_no_P_3 * BB_no * CC_no_Q_3)
M222_4_2 <- sum(AA_yes_P_3 * BB_no * CC_no_Q_3)
M222_4_3 <- sum(AA_no_P_3 * BB * CC_no_Q_3)
M222_4_4 <- sum(AA_no_P_3 * BB_no * CC_yes_Q_3)
M222_4_5 <- sum(AA_yes_P_3 * BB * CC_no_Q_3)
M222_4_6 <- sum(AA_yes_P_3 * BB_no * CC_yes_Q_3)
M222_4_7 <- sum(AA_no_P_3 * BB * CC_yes_Q_3)
M222_4_8 <- sum(AA_yes_P_3 * BB * CC_yes_Q_3)
M222_5_1 <- sum(AA_no_P_4 * BB_no * CC_no_Q_3)
M222_5_2 <- sum(AA_yes_P_4 * BB_no * CC_no_Q_3)
M222_5_3 <- sum(AA_no_P_4 * BB * CC_no_Q_3)
M222_5_4 <- sum(AA_no_P_4 * BB_no * CC_yes_Q_3)
M222_5_5 <- sum(AA_yes_P_4 * BB * CC_no_Q_3)
M222_5_6 <- sum(AA_yes_P_4 * BB_no * CC_yes_Q_3)
M222_5_7 <- sum(AA_no_P_4 * BB * CC_yes_Q_3)
M222_5_8 <- sum(AA_yes_P_4 * BB * CC_yes_Q_3)
M222_6_1 <- mat_tri(AA_no_P_2 * BB_no * CC_no_Q_4)
M222_6_2 <- mat_tri(AA_yes_P_2 * BB_no * CC_no_Q_4)
M222_6_3 <- mat_tri(AA_no_P_2 * BB * CC_no_Q_4)
M222_6_4 <- mat_tri(AA_no_P_2 * BB_no * CC_yes_Q_4)
M222_6_5 <- mat_tri(AA_yes_P_2 * BB * CC_no_Q_4)
M222_6_6 <- mat_tri(AA_yes_P_2 * BB_no * CC_yes_Q_4)
M222_6_7 <- mat_tri(AA_no_P_2 * BB * CC_yes_Q_4)
M222_6_8 <- mat_tri(AA_yes_P_2 * BB * CC_yes_Q_4)
M222_7_1 <- sum(AA_no_P_3 * BB_no * CC_no_Q_4)
M222_7_2 <- sum(AA_yes_P_3 * BB_no * CC_no_Q_4)
M222_7_3 <- sum(AA_no_P_3 * BB * CC_no_Q_4)
M222_7_4 <- sum(AA_no_P_3 * BB_no * CC_yes_Q_4)
M222_7_5 <- sum(AA_yes_P_3 * BB * CC_no_Q_4)
M222_7_6 <- sum(AA_yes_P_3 * BB_no * CC_yes_Q_4)
M222_7_7 <- sum(AA_no_P_3 * BB * CC_yes_Q_4)
M222_7_8 <- sum(AA_yes_P_3 * BB * CC_yes_Q_4)
M222_8_1 <- mat_tri(AA_no_P_4 * BB_no * CC_no_Q_4)
M222_8_2 <- mat_tri(AA_yes_P_4 * BB_no * CC_no_Q_4)
M222_8_3 <- mat_tri(AA_no_P_4 * BB * CC_no_Q_4)
M222_8_4 <- mat_tri(AA_no_P_4 * BB_no * CC_yes_Q_4)
M222_8_5 <- mat_tri(AA_yes_P_4 * BB * CC_no_Q_4)
M222_8_6 <- mat_tri(AA_yes_P_4 * BB_no * CC_yes_Q_4)
M222_8_7 <- mat_tri(AA_no_P_4 * BB * CC_yes_Q_4)
M222_8_8 <- mat_tri(AA_yes_P_4 * BB * CC_yes_Q_4)
M222_9_1 <- sum(AA_no_P_3t * BB_no * CC_no_Q_3)
M222_9_2 <- sum(AA_yes_P_3t * BB_no * CC_no_Q_3)
M222_9_3 <- sum(AA_no_P_3t * BB * CC_no_Q_3)
M222_9_4 <- sum(AA_no_P_3t * BB_no * CC_yes_Q_3)
M222_9_5 <- sum(AA_yes_P_3t * BB * CC_no_Q_3)
M222_9_6 <- sum(AA_yes_P_3t * BB_no * CC_yes_Q_3)
M222_9_7 <- sum(AA_no_P_3t * BB * CC_yes_Q_3)
M222_9_8 <- sum(AA_yes_P_3t * BB * CC_yes_Q_3)
intra_guild_motif <- c(M111,M112_1,M112_2,M211_1,M211_2,M212_1,M212_2,M212_3,M212_4,M121_1,M121_2,M122_1_1,M122_1_2,M122_1_3,M122_1_4,
M122_2_1,M122_2_2,M122_2_3,M122_2_4,M122_3_1,M122_3_2,M122_3_3,M122_3_4,M221_1_1,M221_1_2,M221_1_3,M221_1_4,
M221_2_1,M221_2_2,M221_2_3,M221_2_4,M221_3_1,M221_3_2,M221_3_3,M221_3_4,M222_1_1,M222_1_2,M222_1_3,M222_1_4,
M222_1_5,M222_1_6,M222_1_7,M222_1_8,M222_2_1,M222_2_2,M222_2_3,M222_2_4,M222_2_5,M222_2_6,M222_2_7,M222_2_8,
M222_3_1,M222_3_2,M222_3_3,M222_3_4,M222_3_5,M222_3_6,M222_3_7,M222_3_8,
M222_4_1,M222_4_2,M222_4_3,M222_4_4,M222_4_5,M222_4_6,M222_4_7,M222_4_8,
M222_5_1,M222_5_2,M222_5_3,M222_5_4,M222_5_5,M222_5_6,M222_5_7,M222_5_8,
M222_6_1,M222_6_2,M222_6_3,M222_6_4,M222_6_5,M222_6_6,M222_6_7,M222_6_8,
M222_7_1,M222_7_2,M222_7_3,M222_7_4,M222_7_5,M222_7_6,M222_7_7,M222_7_8,
M222_8_1,M222_8_2,M222_8_3,M222_8_4,M222_8_5,M222_8_6,M222_8_7,M222_8_8,
M222_9_1,M222_9_2,M222_9_3,M222_9_4,M222_9_5,M222_9_6,M222_9_7,M222_9_8)
motif_names<-c("M111","M112-1","M112-2","M211-1","M211-2","M212-1","M212-2","M212-3","M212-4","M121-1","M121-2","M122-1-1","M122-1-2","M122-1-3","M122-1-4",
"M122-2-1","M122-2-2","M122-2-3","M122-2-4","M122-3-1","M122-3-2","M122-3-3","M122-3-4","M221-1-1","M221-1-2","M221-1-3","M221-1-4",
"M221-2-1","M221-2-2","M221-2-3","M221-2-4","M221-3-1","M221-3-2","M221-3-3","M221-3-4","M222-1-1","M222-1-2",'M222-1-3',"M222-1-4",
"M222-1-5","M222-1-6","M222-1-7","M222-1-8","M222-2-1","M222-2-2","M222-2-3","M222-2-4","M222-2-5","M222-2-6","M222-2-7","M222-2-8",
"M222-3-1","M222-3-2","M222-3-3","M222-3-4","M222-3-5","M222-3-6","M222-3-7","M222-3-8",
"M222-4-1","M222-4-2","M222-4-3","M222-4-4","M222-4-5","M222-4-6","M222-4-7","M222-4-8",
"M222-5-1","M222-5-2","M222-5-3","M222-5-4","M222-5-5","M222-5-6","M222-5-7","M222-5-8",
"M222-6-1","M222-6-2","M222-6-3","M222-6-4","M222-6-5","M222-6-6","M222-6-7","M222-6-8",
"M222-7-1","M222-7-2","M222-7-3","M222-7-4","M222-7-5","M222-7-6","M222-7-7","M222-7-8",
"M222-8-1","M222-8-2","M222-8-3","M222-8-4","M222-8-5","M222-8-6","M222-8-7","M222-8-8",
"M222-9-1","M222-9-2","M222-9-3","M222-9-4","M222-9-5","M222-9-6","M222-9-7","M222-9-8")
names( intra_guild_motif)<-motif_names
if(weighted){
All_add <- function(a,b){ return((a!=0)*(b!=0)*(a+b)) }
One_add <- function(a,b){ return((a!=0)*(b!=0)*(a)) }
ObW <- colSums(PW)
RbW <- rowSums(QW)
B2C_NOW <- apply(QW,1,function(x){ A<- apply(CC_no,2,function(y){ One_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
B2C_YESW <- apply(QW,1,function(x){ A<- apply(CCW,2,function(y){ All_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
B2A_NOW <- apply(PW,2,function(x){ A<- apply(AA_no,2,function(y){ One_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
B2A_YESW <- apply(PW,2,function(x){ A<- apply(AAW,2,function(y){ All_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
M111 <- sum(ObW * Rb + RbW * Ob)
M112_1 <- sum( ObW * B2C_NO + B2C_NOW * Ob )
M112_2 <- sum( ObW * B2C_YES + B2C_YESW * Ob )
M211_1 <- sum(B2A_NOW * Rb + RbW * B2A_NO )
M211_2 <- sum(B2A_YESW * Rb + RbW * B2A_YES )
M212_1 <- sum(B2A_NOW * B2C_NO + B2C_NOW *B2A_NO)
M212_2 <- sum(B2A_YESW * B2C_NO + B2C_NOW * B2A_YES)
M212_3 <- sum(B2A_NOW * B2C_YES + B2C_YESW * B2A_NO)
M212_4 <- sum(B2A_YESW * B2C_YES + B2C_YESW * B2A_YES)
A_2BW <- t(apply(PW,2,function(x){apply(PW,2,function(y){ sum(All_add(x,y)) })}))
C_2BW <- t(apply(QW,1,function(x){apply(QW,1,function(y){ sum(All_add(x,y)) })}))
M121_1 <- mat_tri( (A_2BW*Vbb + C_2BW*Ubb) * BB_no)
M121_2 <- mat_tri( (A_2BW*Vbb + C_2BW*Ubb)* BB_two + UVbb * BBW )
PW_all_yes <- t(apply(PW, 2, function(x){A <- (x!=0)%*%t(x); All_add(A,x)})) # All_add(t(All_add(t(All_add(A,x)),x)),PP)
PW_one_yes <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); A }))
PW_two_yes <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); t(A) }))
PW_all_no <- t(apply(PW, 2, function(x){A <- (x!=0)%*%t(x); All_add(A,x) * AA_no})) # All_add(t(All_add(t(All_add(A,x)),x)),PP)
PW_one_no <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); A * AA_no}))
PW_two_no <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); t(A) * AA_no}))
QW_all_yes <- t(apply(QW, 1, function(x){A <- (x!=0)%*%t(x); All_add(A,x)}))
QW_one_yes <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); A}))
QW_two_yes <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); t(A) }))
QW_all_no <- t(apply(QW, 1, function(x){A <- (x!=0)%*%t(x); All_add(A,x)* CC_no}))
QW_one_no <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); A * CC_no}))
QW_two_no <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); t(A) * CC_no}))
AA_no_PW_2 <- t(apply(PW_two_no,1,function(x){apply(PW_one_no,1,function(y){ sum(All_add(x,y))})}))
AA_yes_PW_2 <- t(apply(PW_two_yes,1,function(x){apply(PW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(AA_two)*(x+y+as.vector(AAW)))})}))
AA_no_PW_3 <- t(apply(PW_all_no,1,function(x){apply(PW_one_no,1,function(y){ sum(All_add(x,y))})}))
AA_yes_PW_3 <- t(apply(PW_all_yes,1,function(x){apply(PW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(AA_two)*(x+y+as.vector(AAW)))})}))
AA_no_PW_3t <- t(AA_no_PW_3)
AA_yes_PW_3t <- t(AA_yes_PW_3)
AA_no_PW_4 <- t(apply(PW_all_no,1,function(x){apply(PW_all_no,1,function(y){ sum(All_add(x,y))/2})}))
AA_yes_PW_4 <- t(apply(PW_all_yes,1,function(x){apply(PW_all_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(AA_two)*(x+y+as.vector(AAW))) /2})}))
CC_no_QW_2 <- t(apply(QW_two_no,1,function(x){apply(QW_one_no,1,function(y){ sum(All_add(x,y))})}))
CC_yes_QW_2 <- t(apply(QW_two_yes,1,function(x){apply(QW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(CC_two)*(x+y+as.vector(CCW)))})}))
CC_no_QW_3 <- t(apply(QW_all_no,1,function(x){apply(QW_one_no,1,function(y){ sum(All_add(x,y))})}))
CC_yes_QW_3 <- t(apply(QW_all_yes,1,function(x){apply(QW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(CC_two)*(x+y+as.vector(CCW)))})}))
CC_no_QW_4 <- t(apply(QW_all_no,1,function(x){apply(QW_all_no,1,function(y){ sum(All_add(x,y))/2 })}))
CC_yes_QW_4 <- t(apply(QW_all_yes,1,function(x){apply(QW_all_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(CC_two)*(x+y+as.vector(CCW)))/2 })}))
M122_1_1 <- mat_tri((A_2BW * CC_no_Q_2 + CC_no_QW_2 * Ubb) * BB_no)
M122_1_2 <- mat_tri((A_2BW * CC_no_Q_2 + CC_no_QW_2 * Ubb) * BB_two + Ubb * CC_no_Q_2 * BBW)
M122_1_3 <- mat_tri((A_2BW * CC_yes_Q_2 + CC_yes_QW_2 * Ubb) * BB_no)
M122_1_4 <- mat_tri((A_2BW * CC_yes_Q_2 + CC_yes_QW_2 * Ubb) * BB_two + Ubb * CC_yes_Q_2 * BBW)
M122_2_1 <- sum((A_2BW * CC_no_Q_3 + CC_no_QW_3 * Ubb) * BB_no)
M122_2_2 <- sum((A_2BW * CC_no_Q_3 + CC_no_QW_3 * Ubb) * BB_two + Ubb * CC_no_Q_3 * BBW)
M122_2_3 <- sum((A_2BW * CC_yes_Q_3 + CC_yes_QW_3 * Ubb) * BB_no)
M122_2_4 <- sum((A_2BW * CC_yes_Q_3 + CC_yes_QW_3 * Ubb) * BB_two + Ubb * CC_yes_Q_3 * BBW)
M122_3_1 <- mat_tri((A_2BW * CC_no_Q_4 + CC_no_QW_4 * Ubb) * BB_no)
M122_3_2 <- mat_tri((A_2BW * CC_no_Q_4 + CC_no_QW_4 * Ubb) * BB_two + Ubb * CC_no_Q_4 * BBW)
M122_3_3 <- mat_tri((A_2BW * CC_yes_Q_4 + CC_yes_QW_4 * Ubb) * BB_no)
M122_3_4 <- mat_tri((A_2BW * CC_yes_Q_4 + CC_yes_QW_4 * Ubb) * BB_two + Ubb * CC_yes_Q_4 * BBW)
M221_1_1 <- mat_tri((AA_no_PW_2 * Vbb + C_2BW * AA_no_P_2) * BB_no)
M221_1_2 <- mat_tri((AA_yes_PW_2 * Vbb + C_2BW * AA_yes_P_2) * BB_no)
M221_1_3 <- mat_tri((AA_no_PW_2 * Vbb + C_2BW * AA_no_P_2) * BB_two + AA_no_P_2 * Vbb * BBW)
M221_1_4 <- mat_tri((AA_yes_PW_2 * Vbb + C_2BW * AA_yes_P_2) * BB_two + AA_yes_P_2 * Vbb * BBW)
M221_2_1 <- sum((AA_no_PW_3 * Vbb + C_2BW * AA_no_P_3) * BB_no)
M221_2_2 <- sum((AA_yes_PW_3 * Vbb + C_2BW * AA_yes_P_3) * BB_no)
M221_2_3 <- sum((AA_no_PW_3 * Vbb + C_2BW * AA_no_P_3) * BB_two + AA_no_P_3 * Vbb * BBW)
M221_2_4 <- sum((AA_yes_PW_3 * Vbb + C_2BW * AA_yes_P_3) * BB_two + AA_yes_P_3 * Vbb * BBW)
M221_3_1 <- mat_tri((AA_no_PW_4 * Vbb + C_2BW * AA_no_P_4) * BB_no)
M221_3_2 <- mat_tri((AA_yes_PW_4 * Vbb + C_2BW * AA_yes_P_4) * BB_no)
M221_3_3 <- mat_tri((AA_no_PW_4 * Vbb + C_2BW * AA_no_P_4) * BB_two + AA_no_P_4 * Vbb * BBW)
M221_3_4 <- mat_tri((AA_yes_PW_4 * Vbb + C_2BW * AA_yes_P_4) * BB_two + AA_yes_P_4 * Vbb * BBW)
M222_1_1 <- sum((AA_no_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_3 ) * BB_no )
M222_1_2 <- sum((AA_yes_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_3 ) * BB_no)
M222_1_3 <- sum((AA_no_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_no_Q_2 * BBW )
M222_1_4 <- sum((AA_no_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_3 ) * BB_no)
M222_1_5 <- sum((AA_yes_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_no_Q_2 * BBW )
M222_1_6 <- sum((AA_yes_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_3 ) * BB_no)
M222_1_7 <- sum((AA_no_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_yes_Q_2 * BBW )
M222_1_8 <- sum((AA_yes_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_yes_Q_2 * BBW )
M222_2_1 <- mat_tri((AA_no_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_4 ) * BB_no )
M222_2_2 <- mat_tri((AA_yes_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_4 ) * BB_no)
M222_2_3 <- mat_tri((AA_no_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_no_Q_2 * BBW )
M222_2_4 <- mat_tri((AA_no_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_4 ) * BB_no)
M222_2_5 <- mat_tri((AA_yes_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_no_Q_2 * BBW )
M222_2_6 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_4 ) * BB_no)
M222_2_7 <- mat_tri((AA_no_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_yes_Q_2 * BBW )
M222_2_8 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_yes_Q_2 * BBW )
M222_3_1 <- sum((AA_no_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_2 ) * BB_no )
M222_3_2 <- sum((AA_yes_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_2 ) * BB_no)
M222_3_3 <- sum((AA_no_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_no_Q_3 * BBW )
M222_3_4 <- sum((AA_no_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_2 ) * BB_no)
M222_3_5 <- sum((AA_yes_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_no_Q_3 * BBW )
M222_3_6 <- sum((AA_yes_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_2 ) * BB_no)
M222_3_7 <- sum((AA_no_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_yes_Q_3 * BBW )
M222_3_8 <- sum((AA_yes_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_yes_Q_3 * BBW )
M222_4_1 <- sum((AA_no_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3 ) * BB_no )
M222_4_2 <- sum((AA_yes_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3 ) * BB_no)
M222_4_3 <- sum((AA_no_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_no_Q_3 * BBW )
M222_4_4 <- sum((AA_no_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3 ) * BB_no)
M222_4_5 <- sum((AA_yes_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_no_Q_3 * BBW )
M222_4_6 <- sum((AA_yes_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3 ) * BB_no)
M222_4_7 <- sum((AA_no_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_yes_Q_3 * BBW )
M222_4_8 <- sum((AA_yes_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_yes_Q_3 * BBW )
M222_5_1 <- sum((AA_no_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_4 ) * BB_no )
M222_5_2 <- sum((AA_yes_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_4 ) * BB_no)
M222_5_3 <- sum((AA_no_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_no_Q_3 * BBW )
M222_5_4 <- sum((AA_no_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_4 ) * BB_no)
M222_5_5 <- sum((AA_yes_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_no_Q_3 * BBW )
M222_5_6 <- sum((AA_yes_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_4 ) * BB_no)
M222_5_7 <- sum((AA_no_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_yes_Q_3 * BBW )
M222_5_8 <- sum((AA_yes_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_yes_Q_3 * BBW )
M222_6_1 <- mat_tri((AA_no_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_2 ) * BB_no )
M222_6_2 <- mat_tri((AA_yes_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_2 ) * BB_no)
M222_6_3 <- mat_tri((AA_no_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_no_Q_4 * BBW )
M222_6_4 <- mat_tri((AA_no_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_2 ) * BB_no)
M222_6_5 <- mat_tri((AA_yes_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_no_Q_4 * BBW )
M222_6_6 <- mat_tri((AA_yes_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_2 ) * BB_no)
M222_6_7 <- mat_tri((AA_no_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_yes_Q_4 * BBW )
M222_6_8 <- mat_tri((AA_yes_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_yes_Q_4 * BBW )
M222_7_1 <- sum((AA_no_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_3 ) * BB_no )
M222_7_2 <- sum((AA_yes_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_3 ) * BB_no)
M222_7_3 <- sum((AA_no_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_no_Q_4 * BBW )
M222_7_4 <- sum((AA_no_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_3 ) * BB_no)
M222_7_5 <- sum((AA_yes_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_no_Q_4 * BBW )
M222_7_6 <- sum((AA_yes_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_3 ) * BB_no)
M222_7_7 <- sum((AA_no_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_yes_Q_4 * BBW )
M222_7_8 <- sum((AA_yes_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_yes_Q_4 * BBW )
M222_8_1 <- mat_tri((AA_no_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_4 ) * BB_no )
M222_8_2 <- mat_tri((AA_yes_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_4 ) * BB_no)
M222_8_3 <- mat_tri((AA_no_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_no_Q_4 * BBW )
M222_8_4 <- mat_tri((AA_no_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_4 ) * BB_no)
M222_8_5 <- mat_tri((AA_yes_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_no_Q_4 * BBW )
M222_8_6 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_4 ) * BB_no)
M222_8_7 <- mat_tri((AA_no_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_yes_Q_4 * BBW )
M222_8_8 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_yes_Q_4 * BBW )
M222_9_1 <- sum((AA_no_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3t ) * BB_no )
M222_9_2 <- sum((AA_yes_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3t ) * BB_no)
M222_9_3 <- sum((AA_no_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3t) * BB_two + AA_no_P_3t * CC_no_Q_3 * BBW )
M222_9_4 <- sum((AA_no_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3t ) * BB_no)
M222_9_5 <- sum((AA_yes_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3t) * BB_two + AA_yes_P_3t * CC_no_Q_3 * BBW )
M222_9_6 <- sum((AA_yes_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3t ) * BB_no)
M222_9_7 <- sum((AA_no_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3t) * BB_two + AA_no_P_3t * CC_yes_Q_3 * BBW )
M222_9_8 <- sum((AA_yes_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3t) * BB_two + AA_yes_P_3t * CC_yes_Q_3 * BBW )
motif_weighted <- c(M111,M112_1,M112_2,M211_1,M211_2,M212_1,M212_2,M212_3,M212_4,M121_1,M121_2,M122_1_1,M122_1_2,M122_1_3,M122_1_4,
M122_2_1,M122_2_2,M122_2_3,M122_2_4,M122_3_1,M122_3_2,M122_3_3,M122_3_4,M221_1_1,M221_1_2,M221_1_3,M221_1_4,
M221_2_1,M221_2_2,M221_2_3,M221_2_4,M221_3_1,M221_3_2,M221_3_3,M221_3_4,M222_1_1,M222_1_2,M222_1_3,M222_1_4,
M222_1_5,M222_1_6,M222_1_7,M222_1_8,M222_2_1,M222_2_2,M222_2_3,M222_2_4,M222_2_5,M222_2_6,M222_2_7,M222_2_8,
M222_3_1,M222_3_2,M222_3_3,M222_3_4,M222_3_5,M222_3_6,M222_3_7,M222_3_8,
M222_4_1,M222_4_2,M222_4_3,M222_4_4,M222_4_5,M222_4_6,M222_4_7,M222_4_8,
M222_5_1,M222_5_2,M222_5_3,M222_5_4,M222_5_5,M222_5_6,M222_5_7,M222_5_8,
M222_6_1,M222_6_2,M222_6_3,M222_6_4,M222_6_5,M222_6_6,M222_6_7,M222_6_8,
M222_7_1,M222_7_2,M222_7_3,M222_7_4,M222_7_5,M222_7_6,M222_7_7,M222_7_8,
M222_8_1,M222_8_2,M222_8_3,M222_8_4,M222_8_5,M222_8_6,M222_8_7,M222_8_8,
M222_9_1,M222_9_2,M222_9_3,M222_9_4,M222_9_5,M222_9_6,M222_9_7,M222_9_8)
intra_guild_edge <- c(2, 3, 4, 3, 4, 4, 5, 5, 6, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7,
8, 5, 6, 6, 6, 7, 7, 7, 8, 6, 7, 7, 7, 8, 8, 8, 9, 5, 6, 6, 6, 7, 7, 7, 8, 6, 7, 7, 7, 8, 8, 8, 9, 7, 8, 8, 8, 9, 9, 9,
10, 6, 7, 7, 7, 8, 8, 8, 9, 7, 8, 8, 8, 9, 9, 9, 10, 8, 9, 9, 9, 10, 10, 10, 11, 6, 7, 7, 7, 8, 8, 8, 9)
mean_weighted <- motif_weighted/(intra_guild_motif * intra_guild_edge)
mean_weighted <- replace(mean_weighted,which(is.nan(mean_weighted)),NA)
names(mean_weighted)<-motif_names
return(list(intra_guild_icmotif=intra_guild_motif,mean_weight=mean_weighted))
}
else{
names(intra_guild_motif)<-motif_names
return(intra_guild_motif)
}
}
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Defines functions ig_icmotif_count
Documented in ig_icmotif_count
#' Count interconnection motifs for tripartite networks with intra-guild interactions
#'
#' Counting the frequencies of interconnection motifs for a tripartite interaction network with intra-guild interactions.
#'
#' @param mat A square block interaction matrix representing a tripartite network including intra-guild and inter-guild interactions. See details.
#' @param guilds A character vector matching rows of \code{mat} to indicate the guilds using ('a','b' and 'c'). See details.
#' @param weighted Logical. Default to FALSE. If TRUE, the arithmetic mean of the subgraph weights is provided for each motif. See details
#' @import igraph
#'
#' @encoding UTF-8
#'
#' @export
#'
#' @details
#' This function is designed for tripartite networks with intra-guild interactions. The input network should be nput as a block matrix (\eqn{M}) to represent three groups of nodes (a-nodes, b-nodes and c-nodes): three intra-guild interaction matrices (\eqn{m_{aa},m_{bb},m_{cc}}),
#' two inter-guild matrices of a and b-nodes (\eqn{m_{ab},m_{ba}}), and two inter-guild matrices of b- and c-nodes(\eqn{m_{bc},m_{cb}}).
#' \deqn{
#' \left(
#' \begin{array}{ccc}
#' m_{aa} & m_{ab} & 0 \\
#' m_{ba} & m_{bb} & m_{bc} \\
#' 0 & m_{cb} & m_{cc}
#' \end{array}
#' \right)
#' }
#'
#' \code{guilds} should be a vector of the same length as the row of \code{mat} like c("a","a"..."b","b"..."c","c"..)
#'
#' \strong{Interconnection motifs in tripartite networks with intra-guild interactions}
#' <br>An interconnection motif is defined to comprise three sets of connected nodes: the connector nodes (belonging to b-nodes), the nodes in one subnetwork (belonging to a-nodes in the P subnetwork), and the nodes in the other subnetwork (belonging to c-nodes in the Q subnetwork). Each guild has two nodes at most, resulting in a total of 107 distinct motif forms.
#' The algorithm for counting interconnection motifs is designed by extending the fast approach from Simmons et al.(2019). For interconnection motifs in tripartite networks without intra-guild interactions, please see **icmotif_count** and **icmotif_role**.
#'
#' \strong{Weighted networks}
#' <br>For weighted tripartite networks, the mean weight of a given motif is provided by averaging the weights of all motif occurrences isomorphic to the motif. The weight of a motif occurrence is the arithmetic mean of the weights of its links, following Mora et al. (2018) and Simmons et al. (2019).
#'
#'
#' @return
#' Return a matrix of counts (and mean weight) of 107 interconnection motifs.
#'
#'
#' @references
#' Garcia-Callejas, D., Godoy, O., Buche, L., Hurtado, M., Lanuza, J.B., Allen-Perkins, A. et al. (2023) Non-random interactions within and across guilds shape the potential to coexist in multi-trophic ecological communities. Ecology Letters, 26, 831-842.
#'
#' Pilosof, S., Porter, M. A., Pascual, M., & KC)fi, S. (2017). The multilayer nature of ecological networks. Nature Ecology & Evolution, 1(4), 0101.
#'
#' Mora, B.B., Cirtwill, A.R. and Stouffer, D.B. (2018). pymfinder: a tool for the motif analysis of binary and quantitative complex networks. bioRxiv, 364703.
#'
#' Simmons, B. I., Sweering, M. J., Schillinger, M., Dicks, L. V., Sutherland, W. J., & Di Clemente, R. (2019). bmotif: A package for motif analyses of bipartite networks. Methods in Ecology and Evolution, 10(5), 695-701.
#'
#' @examples
#'
#' ##A toy tripartite network with intra-guild negative interactions:
#' ##Inter-guild mutualistic interactions and inter-guild antagonistic interactions.
#' set.seed(12)
#' ##4 a-nodes, 5 b-nodes, and 3 c-nodes
#'
#' ##Intra-guild interaction matrices
#' mat_aa<-matrix(runif(16,-0.8,-0.2),4,4)
#' mat_aa <- mat_aa + t(mat_aa); diag(mat_aa) <- 0
#' mat_bb<-matrix(runif(25,-0.8,-0.2),5,5)
#' mat_bb <- mat_bb + t(mat_bb); diag(mat_bb) <- 0
#' mat_cc<-matrix(runif(9,-0.8,-0.2),3,3)
#' mat_cc <- mat_cc + t(mat_cc); diag(mat_cc) <- 0
#'
#' ##Inter-guild interaction matrices between a- and b-nodes.
#' mat_ab<-mat_ba<-matrix(sample(c(rep(0,8),runif(12,0,0.5))),4,5,byrow=TRUE)
#' mat_ba<-t(mat_ba)
#'
#' ##Inter-guild interaction matrices between b- and c-nodes.
#' mat_cb<-mat_bc<-matrix(sample(c(rep(0,8),runif(7,0,0.5))),3,5,byrow=TRUE)
#' mat_bc<--t(mat_bc)
#' mat<-rbind(cbind(mat_aa,mat_ab,matrix(0,4,3)),cbind(mat_ba,mat_bb,mat_bc))
#' mat<-rbind(mat,cbind(matrix(0,3,4),mat_cb,mat_cc))
#'
#' ##set the node names
#' rownames(mat)<-c(paste0("a",1:4),paste0("b",1:5),paste0("c",1:3))
#' colnames(mat)<-c(paste0("a",1:4),paste0("b",1:5),paste0("c",1:3))
#'
#' #mat[mat!=0] <- 1
#' myguilds=c(rep("a",4),rep("b",5),rep("c",3))
#' ig_icmotif_count(mat,guilds=myguilds,TRUE)
#'
#'
ig_icmotif_count <-
function(mat, guilds,weighted =FALSE) {
if (inherits(mat, c("matrix", "data.frame")) == T || ncol(mat)==nrow(mat)){
if(length(guilds)!= nrow(mat))
stop("guilds should be a vector of the same length as the row of mat!")
else{
if(sum(unique(guilds)%in%c("a","b","c"))!=3)
stop("guilds should be composed of these three characters (a,b,c)!")
else{
if(is.null(dimnames(mat)) || sum(rownames(mat)!=colnames(mat))!=0 )
stop("Make sure this matrix either have the same row and column names [No NA!!!]")
else{
mat <- abs(mat)
subnet_mat1 <- mat[guilds == "a", guilds == "b"]
subnet_mat2 <- mat[guilds == "b", guilds == "c"]
AA <- mat[guilds == "a", guilds == "a"]
BB <- mat[guilds == "b", guilds == "b"]
CC <- mat[guilds == "c", guilds == "c"]
}
}
}
}
else
stop("mat should be a square block interaction matrix!")
dimnames(subnet_mat1) <- NULL
dimnames(subnet_mat2) <- NULL
P <- subnet_mat1
Q <- subnet_mat2
PW <- P; QW <- Q; AAW <- AA; BBW <- BB; CCW <- CC
AA <- (AA!=0)*1; BB <- (BB!=0)*1; CC <- (CC!=0)*1
P <- (P!=0)*1; Q <- (Q!=0)*1
AA_no <- AA == 0
diag(AA) <- 0
diag(AA_no) <- 0
AA_two <- (AA!=0)*1
BB_no <- BB == 0
diag(BB) <- 0
diag(BB_no) <- 0
BB_two <- (BB!=0)*1
CC_no <- CC == 0
diag(CC) <- 0
diag(CC_no) <- 0
CC_two <- (CC!=0)*1
Ob <- colSums(P); Rb <- rowSums(Q)
Ubb <- t(P) %*% P
Vbb <- Q %*% t(Q)
UVbb <- Ubb * Vbb
B2C_NO <- rowSums((Q%*%CC_no) *Q) /2
B2C_YES <- rowSums((Q%*%CC_two) *Q) /2
B2A_NO <- rowSums((t(P)%*%AA_no) *t(P)) /2
B2A_YES <- rowSums((t(P)%*%AA_two) *t(P)) /2
M111 <- sum(Ob * Rb)
M112_1 <- sum(Ob * B2C_NO)
M112_2 <- sum(Ob * B2C_YES)
M211_1 <- sum(B2A_NO * Rb)
M211_2 <- sum(B2A_YES * Rb)
M212_1 <- sum(B2A_NO * B2C_NO)
M212_2 <- sum(B2A_YES * B2C_NO)
M212_3 <- sum(B2A_NO * B2C_YES)
M212_4 <- sum(B2A_YES * B2C_YES)
mat_tri <- function(mat) {sum(mat[upper.tri(mat)])}
M121_1 <- mat_tri(UVbb * BB_no)
M121_2 <- mat_tri(UVbb * BB_two)
P_all_yes <- t(apply(P, 2, function(x) { A <- x %*% t(x); A * AA}))
P_one_yes <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); A *AA}))
P_two_yes <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); t(A) *AA}))
P_all_no <- t(apply(P, 2, function(x) { A <- x %*% t(x); A * AA_no}))
P_one_no <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); A * AA_no}))
P_two_no <- t(apply(P, 2, function(x) { A <- (x == 0) %*% t(x); t(A) * AA_no}))
Q_all_yes <- t(apply(Q, 1, function(x) { A <- x %*% t(x); A * CC}))
Q_one_yes <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); A * CC}))
Q_two_yes <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); t(A) * CC}))
Q_all_no <- t(apply(Q, 1, function(x) { A <- x %*% t(x); A * CC_no}))
Q_one_no <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); A * CC_no}))
Q_two_no <- t(apply(Q, 1, function(x) { A <- (x == 0) %*% t(x); t(A) * CC_no}))
AA_no_P_2 <- P_two_no %*% t(P_one_no)
AA_yes_P_2 <- P_two_yes %*% t(P_one_yes)
AA_no_P_3 <- P_all_no %*% t(P_one_no)
AA_yes_P_3 <- P_all_yes %*% t(P_one_yes)
AA_no_P_3t <- t(AA_no_P_3)
AA_yes_P_3t <- t(AA_yes_P_3)
AA_no_P_4 <- (P_all_no %*% t(P_all_no)) / 2
AA_yes_P_4 <- (P_all_yes %*% t(P_all_yes)) / 2
CC_no_Q_2 <- Q_two_no %*% t(Q_one_no)
CC_yes_Q_2 <- Q_two_yes %*% t(Q_one_yes)
CC_no_Q_3 <- Q_all_no %*% t(Q_one_no)
CC_yes_Q_3 <- Q_all_yes %*% t(Q_one_yes)
CC_no_Q_4 <- (Q_all_no %*% t(Q_all_no)) / 2
CC_yes_Q_4 <- (Q_all_yes %*% t(Q_all_yes)) / 2
M122_1_1 <- mat_tri(Ubb * BB_no * CC_no_Q_2)
M122_1_2 <- mat_tri(Ubb * BB * CC_no_Q_2)
M122_1_3 <- mat_tri(Ubb * BB_no * CC_yes_Q_2)
M122_1_4 <- mat_tri(Ubb * BB * CC_yes_Q_2)
M122_2_1 <- sum(Ubb * BB_no * CC_no_Q_3)
M122_2_2 <- sum(Ubb * BB * CC_no_Q_3)
M122_2_3 <- sum(Ubb * BB_no * CC_yes_Q_3)
M122_2_4 <- sum(Ubb * BB * CC_yes_Q_3)
M122_3_1 <- mat_tri(Ubb * BB_no * CC_no_Q_4)
M122_3_2 <- mat_tri(Ubb * BB * CC_no_Q_4)
M122_3_3 <- mat_tri(Ubb * BB_no * CC_yes_Q_4)
M122_3_4 <- mat_tri(Ubb * BB * CC_yes_Q_4)
M221_1_1 <- mat_tri(AA_no_P_2 * BB_no * Vbb)
M221_1_2 <- mat_tri(AA_yes_P_2 * BB_no * Vbb)
M221_1_3 <- mat_tri(AA_no_P_2 * BB * Vbb)
M221_1_4 <- mat_tri(AA_yes_P_2 * BB * Vbb)
M221_2_1 <- sum(AA_no_P_3 * BB_no * Vbb)
M221_2_2 <- sum(AA_yes_P_3 * BB_no * Vbb)
M221_2_3 <- sum(AA_no_P_3 * BB * Vbb)
M221_2_4 <- sum(AA_yes_P_3 * BB * Vbb)
M221_3_1 <- mat_tri(AA_no_P_4 * BB_no * Vbb)
M221_3_2 <- mat_tri(AA_yes_P_4 * BB_no * Vbb)
M221_3_3 <- mat_tri(AA_no_P_4 * BB * Vbb)
M221_3_4 <- mat_tri(AA_yes_P_4 * BB * Vbb)
M222_1_1 <- sum(AA_no_P_3 * BB_no * CC_no_Q_2)
M222_1_2 <- sum(AA_yes_P_3 * BB_no * CC_no_Q_2)
M222_1_3 <- sum(AA_no_P_3 * BB * CC_no_Q_2)
M222_1_4 <- sum(AA_no_P_3 * BB_no * CC_yes_Q_2)
M222_1_5 <- sum(AA_yes_P_3 * BB * CC_no_Q_2)
M222_1_6 <- sum(AA_yes_P_3 * BB_no * CC_yes_Q_2)
M222_1_7 <- sum(AA_no_P_3 * BB * CC_yes_Q_2)
M222_1_8 <- sum(AA_yes_P_3 * BB * CC_yes_Q_2)
M222_2_1 <- mat_tri(AA_no_P_4 * BB_no * CC_no_Q_2)
M222_2_2 <- mat_tri(AA_yes_P_4 * BB_no * CC_no_Q_2)
M222_2_3 <- mat_tri(AA_no_P_4 * BB * CC_no_Q_2)
M222_2_4 <- mat_tri(AA_no_P_4 * BB_no * CC_yes_Q_2)
M222_2_5 <- mat_tri(AA_yes_P_4 * BB * CC_no_Q_2)
M222_2_6 <- mat_tri(AA_yes_P_4 * BB_no * CC_yes_Q_2)
M222_2_7 <- mat_tri(AA_no_P_4 * BB * CC_yes_Q_2)
M222_2_8 <- mat_tri(AA_yes_P_4 * BB * CC_yes_Q_2)
M222_3_1 <- sum(AA_no_P_2 * BB_no * CC_no_Q_3)
M222_3_2 <- sum(AA_yes_P_2 * BB_no * CC_no_Q_3)
M222_3_3 <- sum(AA_no_P_2 * BB * CC_no_Q_3)
M222_3_4 <- sum(AA_no_P_2 * BB_no * CC_yes_Q_3)
M222_3_5 <- sum(AA_yes_P_2 * BB * CC_no_Q_3)
M222_3_6 <- sum(AA_yes_P_2 * BB_no * CC_yes_Q_3)
M222_3_7 <- sum(AA_no_P_2 * BB * CC_yes_Q_3)
M222_3_8 <- sum(AA_yes_P_2 * BB * CC_yes_Q_3)
M222_4_1 <- sum(AA_no_P_3 * BB_no * CC_no_Q_3)
M222_4_2 <- sum(AA_yes_P_3 * BB_no * CC_no_Q_3)
M222_4_3 <- sum(AA_no_P_3 * BB * CC_no_Q_3)
M222_4_4 <- sum(AA_no_P_3 * BB_no * CC_yes_Q_3)
M222_4_5 <- sum(AA_yes_P_3 * BB * CC_no_Q_3)
M222_4_6 <- sum(AA_yes_P_3 * BB_no * CC_yes_Q_3)
M222_4_7 <- sum(AA_no_P_3 * BB * CC_yes_Q_3)
M222_4_8 <- sum(AA_yes_P_3 * BB * CC_yes_Q_3)
M222_5_1 <- sum(AA_no_P_4 * BB_no * CC_no_Q_3)
M222_5_2 <- sum(AA_yes_P_4 * BB_no * CC_no_Q_3)
M222_5_3 <- sum(AA_no_P_4 * BB * CC_no_Q_3)
M222_5_4 <- sum(AA_no_P_4 * BB_no * CC_yes_Q_3)
M222_5_5 <- sum(AA_yes_P_4 * BB * CC_no_Q_3)
M222_5_6 <- sum(AA_yes_P_4 * BB_no * CC_yes_Q_3)
M222_5_7 <- sum(AA_no_P_4 * BB * CC_yes_Q_3)
M222_5_8 <- sum(AA_yes_P_4 * BB * CC_yes_Q_3)
M222_6_1 <- mat_tri(AA_no_P_2 * BB_no * CC_no_Q_4)
M222_6_2 <- mat_tri(AA_yes_P_2 * BB_no * CC_no_Q_4)
M222_6_3 <- mat_tri(AA_no_P_2 * BB * CC_no_Q_4)
M222_6_4 <- mat_tri(AA_no_P_2 * BB_no * CC_yes_Q_4)
M222_6_5 <- mat_tri(AA_yes_P_2 * BB * CC_no_Q_4)
M222_6_6 <- mat_tri(AA_yes_P_2 * BB_no * CC_yes_Q_4)
M222_6_7 <- mat_tri(AA_no_P_2 * BB * CC_yes_Q_4)
M222_6_8 <- mat_tri(AA_yes_P_2 * BB * CC_yes_Q_4)
M222_7_1 <- sum(AA_no_P_3 * BB_no * CC_no_Q_4)
M222_7_2 <- sum(AA_yes_P_3 * BB_no * CC_no_Q_4)
M222_7_3 <- sum(AA_no_P_3 * BB * CC_no_Q_4)
M222_7_4 <- sum(AA_no_P_3 * BB_no * CC_yes_Q_4)
M222_7_5 <- sum(AA_yes_P_3 * BB * CC_no_Q_4)
M222_7_6 <- sum(AA_yes_P_3 * BB_no * CC_yes_Q_4)
M222_7_7 <- sum(AA_no_P_3 * BB * CC_yes_Q_4)
M222_7_8 <- sum(AA_yes_P_3 * BB * CC_yes_Q_4)
M222_8_1 <- mat_tri(AA_no_P_4 * BB_no * CC_no_Q_4)
M222_8_2 <- mat_tri(AA_yes_P_4 * BB_no * CC_no_Q_4)
M222_8_3 <- mat_tri(AA_no_P_4 * BB * CC_no_Q_4)
M222_8_4 <- mat_tri(AA_no_P_4 * BB_no * CC_yes_Q_4)
M222_8_5 <- mat_tri(AA_yes_P_4 * BB * CC_no_Q_4)
M222_8_6 <- mat_tri(AA_yes_P_4 * BB_no * CC_yes_Q_4)
M222_8_7 <- mat_tri(AA_no_P_4 * BB * CC_yes_Q_4)
M222_8_8 <- mat_tri(AA_yes_P_4 * BB * CC_yes_Q_4)
M222_9_1 <- sum(AA_no_P_3t * BB_no * CC_no_Q_3)
M222_9_2 <- sum(AA_yes_P_3t * BB_no * CC_no_Q_3)
M222_9_3 <- sum(AA_no_P_3t * BB * CC_no_Q_3)
M222_9_4 <- sum(AA_no_P_3t * BB_no * CC_yes_Q_3)
M222_9_5 <- sum(AA_yes_P_3t * BB * CC_no_Q_3)
M222_9_6 <- sum(AA_yes_P_3t * BB_no * CC_yes_Q_3)
M222_9_7 <- sum(AA_no_P_3t * BB * CC_yes_Q_3)
M222_9_8 <- sum(AA_yes_P_3t * BB * CC_yes_Q_3)
intra_guild_motif <- c(M111,M112_1,M112_2,M211_1,M211_2,M212_1,M212_2,M212_3,M212_4,M121_1,M121_2,M122_1_1,M122_1_2,M122_1_3,M122_1_4,
M122_2_1,M122_2_2,M122_2_3,M122_2_4,M122_3_1,M122_3_2,M122_3_3,M122_3_4,M221_1_1,M221_1_2,M221_1_3,M221_1_4,
M221_2_1,M221_2_2,M221_2_3,M221_2_4,M221_3_1,M221_3_2,M221_3_3,M221_3_4,M222_1_1,M222_1_2,M222_1_3,M222_1_4,
M222_1_5,M222_1_6,M222_1_7,M222_1_8,M222_2_1,M222_2_2,M222_2_3,M222_2_4,M222_2_5,M222_2_6,M222_2_7,M222_2_8,
M222_3_1,M222_3_2,M222_3_3,M222_3_4,M222_3_5,M222_3_6,M222_3_7,M222_3_8,
M222_4_1,M222_4_2,M222_4_3,M222_4_4,M222_4_5,M222_4_6,M222_4_7,M222_4_8,
M222_5_1,M222_5_2,M222_5_3,M222_5_4,M222_5_5,M222_5_6,M222_5_7,M222_5_8,
M222_6_1,M222_6_2,M222_6_3,M222_6_4,M222_6_5,M222_6_6,M222_6_7,M222_6_8,
M222_7_1,M222_7_2,M222_7_3,M222_7_4,M222_7_5,M222_7_6,M222_7_7,M222_7_8,
M222_8_1,M222_8_2,M222_8_3,M222_8_4,M222_8_5,M222_8_6,M222_8_7,M222_8_8,
M222_9_1,M222_9_2,M222_9_3,M222_9_4,M222_9_5,M222_9_6,M222_9_7,M222_9_8)
motif_names<-c("M111","M112-1","M112-2","M211-1","M211-2","M212-1","M212-2","M212-3","M212-4","M121-1","M121-2","M122-1-1","M122-1-2","M122-1-3","M122-1-4",
"M122-2-1","M122-2-2","M122-2-3","M122-2-4","M122-3-1","M122-3-2","M122-3-3","M122-3-4","M221-1-1","M221-1-2","M221-1-3","M221-1-4",
"M221-2-1","M221-2-2","M221-2-3","M221-2-4","M221-3-1","M221-3-2","M221-3-3","M221-3-4","M222-1-1","M222-1-2",'M222-1-3',"M222-1-4",
"M222-1-5","M222-1-6","M222-1-7","M222-1-8","M222-2-1","M222-2-2","M222-2-3","M222-2-4","M222-2-5","M222-2-6","M222-2-7","M222-2-8",
"M222-3-1","M222-3-2","M222-3-3","M222-3-4","M222-3-5","M222-3-6","M222-3-7","M222-3-8",
"M222-4-1","M222-4-2","M222-4-3","M222-4-4","M222-4-5","M222-4-6","M222-4-7","M222-4-8",
"M222-5-1","M222-5-2","M222-5-3","M222-5-4","M222-5-5","M222-5-6","M222-5-7","M222-5-8",
"M222-6-1","M222-6-2","M222-6-3","M222-6-4","M222-6-5","M222-6-6","M222-6-7","M222-6-8",
"M222-7-1","M222-7-2","M222-7-3","M222-7-4","M222-7-5","M222-7-6","M222-7-7","M222-7-8",
"M222-8-1","M222-8-2","M222-8-3","M222-8-4","M222-8-5","M222-8-6","M222-8-7","M222-8-8",
"M222-9-1","M222-9-2","M222-9-3","M222-9-4","M222-9-5","M222-9-6","M222-9-7","M222-9-8")
names( intra_guild_motif)<-motif_names
if(weighted){
All_add <- function(a,b){ return((a!=0)*(b!=0)*(a+b)) }
One_add <- function(a,b){ return((a!=0)*(b!=0)*(a)) }
ObW <- colSums(PW)
RbW <- rowSums(QW)
B2C_NOW <- apply(QW,1,function(x){ A<- apply(CC_no,2,function(y){ One_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
B2C_YESW <- apply(QW,1,function(x){ A<- apply(CCW,2,function(y){ All_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
B2A_NOW <- apply(PW,2,function(x){ A<- apply(AA_no,2,function(y){ One_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
B2A_YESW <- apply(PW,2,function(x){ A<- apply(AAW,2,function(y){ All_add(x,y) }); return(sum(All_add(x,t(A)))/2)})
M111 <- sum(ObW * Rb + RbW * Ob)
M112_1 <- sum( ObW * B2C_NO + B2C_NOW * Ob )
M112_2 <- sum( ObW * B2C_YES + B2C_YESW * Ob )
M211_1 <- sum(B2A_NOW * Rb + RbW * B2A_NO )
M211_2 <- sum(B2A_YESW * Rb + RbW * B2A_YES )
M212_1 <- sum(B2A_NOW * B2C_NO + B2C_NOW *B2A_NO)
M212_2 <- sum(B2A_YESW * B2C_NO + B2C_NOW * B2A_YES)
M212_3 <- sum(B2A_NOW * B2C_YES + B2C_YESW * B2A_NO)
M212_4 <- sum(B2A_YESW * B2C_YES + B2C_YESW * B2A_YES)
A_2BW <- t(apply(PW,2,function(x){apply(PW,2,function(y){ sum(All_add(x,y)) })}))
C_2BW <- t(apply(QW,1,function(x){apply(QW,1,function(y){ sum(All_add(x,y)) })}))
M121_1 <- mat_tri( (A_2BW*Vbb + C_2BW*Ubb) * BB_no)
M121_2 <- mat_tri( (A_2BW*Vbb + C_2BW*Ubb)* BB_two + UVbb * BBW )
PW_all_yes <- t(apply(PW, 2, function(x){A <- (x!=0)%*%t(x); All_add(A,x)})) # All_add(t(All_add(t(All_add(A,x)),x)),PP)
PW_one_yes <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); A }))
PW_two_yes <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); t(A) }))
PW_all_no <- t(apply(PW, 2, function(x){A <- (x!=0)%*%t(x); All_add(A,x) * AA_no})) # All_add(t(All_add(t(All_add(A,x)),x)),PP)
PW_one_no <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); A * AA_no}))
PW_two_no <- t(apply(PW, 2, function(x){A <- (x==0)%*%t(x); t(A) * AA_no}))
QW_all_yes <- t(apply(QW, 1, function(x){A <- (x!=0)%*%t(x); All_add(A,x)}))
QW_one_yes <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); A}))
QW_two_yes <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); t(A) }))
QW_all_no <- t(apply(QW, 1, function(x){A <- (x!=0)%*%t(x); All_add(A,x)* CC_no}))
QW_one_no <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); A * CC_no}))
QW_two_no <- t(apply(QW, 1, function(x){A <- (x==0)%*%t(x); t(A) * CC_no}))
AA_no_PW_2 <- t(apply(PW_two_no,1,function(x){apply(PW_one_no,1,function(y){ sum(All_add(x,y))})}))
AA_yes_PW_2 <- t(apply(PW_two_yes,1,function(x){apply(PW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(AA_two)*(x+y+as.vector(AAW)))})}))
AA_no_PW_3 <- t(apply(PW_all_no,1,function(x){apply(PW_one_no,1,function(y){ sum(All_add(x,y))})}))
AA_yes_PW_3 <- t(apply(PW_all_yes,1,function(x){apply(PW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(AA_two)*(x+y+as.vector(AAW)))})}))
AA_no_PW_3t <- t(AA_no_PW_3)
AA_yes_PW_3t <- t(AA_yes_PW_3)
AA_no_PW_4 <- t(apply(PW_all_no,1,function(x){apply(PW_all_no,1,function(y){ sum(All_add(x,y))/2})}))
AA_yes_PW_4 <- t(apply(PW_all_yes,1,function(x){apply(PW_all_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(AA_two)*(x+y+as.vector(AAW))) /2})}))
CC_no_QW_2 <- t(apply(QW_two_no,1,function(x){apply(QW_one_no,1,function(y){ sum(All_add(x,y))})}))
CC_yes_QW_2 <- t(apply(QW_two_yes,1,function(x){apply(QW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(CC_two)*(x+y+as.vector(CCW)))})}))
CC_no_QW_3 <- t(apply(QW_all_no,1,function(x){apply(QW_one_no,1,function(y){ sum(All_add(x,y))})}))
CC_yes_QW_3 <- t(apply(QW_all_yes,1,function(x){apply(QW_one_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(CC_two)*(x+y+as.vector(CCW)))})}))
CC_no_QW_4 <- t(apply(QW_all_no,1,function(x){apply(QW_all_no,1,function(y){ sum(All_add(x,y))/2 })}))
CC_yes_QW_4 <- t(apply(QW_all_yes,1,function(x){apply(QW_all_yes,1,function(y){ sum((x!=0)*(y!=0)*as.vector(CC_two)*(x+y+as.vector(CCW)))/2 })}))
M122_1_1 <- mat_tri((A_2BW * CC_no_Q_2 + CC_no_QW_2 * Ubb) * BB_no)
M122_1_2 <- mat_tri((A_2BW * CC_no_Q_2 + CC_no_QW_2 * Ubb) * BB_two + Ubb * CC_no_Q_2 * BBW)
M122_1_3 <- mat_tri((A_2BW * CC_yes_Q_2 + CC_yes_QW_2 * Ubb) * BB_no)
M122_1_4 <- mat_tri((A_2BW * CC_yes_Q_2 + CC_yes_QW_2 * Ubb) * BB_two + Ubb * CC_yes_Q_2 * BBW)
M122_2_1 <- sum((A_2BW * CC_no_Q_3 + CC_no_QW_3 * Ubb) * BB_no)
M122_2_2 <- sum((A_2BW * CC_no_Q_3 + CC_no_QW_3 * Ubb) * BB_two + Ubb * CC_no_Q_3 * BBW)
M122_2_3 <- sum((A_2BW * CC_yes_Q_3 + CC_yes_QW_3 * Ubb) * BB_no)
M122_2_4 <- sum((A_2BW * CC_yes_Q_3 + CC_yes_QW_3 * Ubb) * BB_two + Ubb * CC_yes_Q_3 * BBW)
M122_3_1 <- mat_tri((A_2BW * CC_no_Q_4 + CC_no_QW_4 * Ubb) * BB_no)
M122_3_2 <- mat_tri((A_2BW * CC_no_Q_4 + CC_no_QW_4 * Ubb) * BB_two + Ubb * CC_no_Q_4 * BBW)
M122_3_3 <- mat_tri((A_2BW * CC_yes_Q_4 + CC_yes_QW_4 * Ubb) * BB_no)
M122_3_4 <- mat_tri((A_2BW * CC_yes_Q_4 + CC_yes_QW_4 * Ubb) * BB_two + Ubb * CC_yes_Q_4 * BBW)
M221_1_1 <- mat_tri((AA_no_PW_2 * Vbb + C_2BW * AA_no_P_2) * BB_no)
M221_1_2 <- mat_tri((AA_yes_PW_2 * Vbb + C_2BW * AA_yes_P_2) * BB_no)
M221_1_3 <- mat_tri((AA_no_PW_2 * Vbb + C_2BW * AA_no_P_2) * BB_two + AA_no_P_2 * Vbb * BBW)
M221_1_4 <- mat_tri((AA_yes_PW_2 * Vbb + C_2BW * AA_yes_P_2) * BB_two + AA_yes_P_2 * Vbb * BBW)
M221_2_1 <- sum((AA_no_PW_3 * Vbb + C_2BW * AA_no_P_3) * BB_no)
M221_2_2 <- sum((AA_yes_PW_3 * Vbb + C_2BW * AA_yes_P_3) * BB_no)
M221_2_3 <- sum((AA_no_PW_3 * Vbb + C_2BW * AA_no_P_3) * BB_two + AA_no_P_3 * Vbb * BBW)
M221_2_4 <- sum((AA_yes_PW_3 * Vbb + C_2BW * AA_yes_P_3) * BB_two + AA_yes_P_3 * Vbb * BBW)
M221_3_1 <- mat_tri((AA_no_PW_4 * Vbb + C_2BW * AA_no_P_4) * BB_no)
M221_3_2 <- mat_tri((AA_yes_PW_4 * Vbb + C_2BW * AA_yes_P_4) * BB_no)
M221_3_3 <- mat_tri((AA_no_PW_4 * Vbb + C_2BW * AA_no_P_4) * BB_two + AA_no_P_4 * Vbb * BBW)
M221_3_4 <- mat_tri((AA_yes_PW_4 * Vbb + C_2BW * AA_yes_P_4) * BB_two + AA_yes_P_4 * Vbb * BBW)
M222_1_1 <- sum((AA_no_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_3 ) * BB_no )
M222_1_2 <- sum((AA_yes_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_3 ) * BB_no)
M222_1_3 <- sum((AA_no_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_no_Q_2 * BBW )
M222_1_4 <- sum((AA_no_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_3 ) * BB_no)
M222_1_5 <- sum((AA_yes_PW_3 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_no_Q_2 * BBW )
M222_1_6 <- sum((AA_yes_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_3 ) * BB_no)
M222_1_7 <- sum((AA_no_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_yes_Q_2 * BBW )
M222_1_8 <- sum((AA_yes_PW_3 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_yes_Q_2 * BBW )
M222_2_1 <- mat_tri((AA_no_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_4 ) * BB_no )
M222_2_2 <- mat_tri((AA_yes_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_4 ) * BB_no)
M222_2_3 <- mat_tri((AA_no_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_no_Q_2 * BBW )
M222_2_4 <- mat_tri((AA_no_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_4 ) * BB_no)
M222_2_5 <- mat_tri((AA_yes_PW_4 * CC_no_Q_2 + CC_no_QW_2 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_no_Q_2 * BBW )
M222_2_6 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_4 ) * BB_no)
M222_2_7 <- mat_tri((AA_no_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_yes_Q_2 * BBW )
M222_2_8 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_2 + CC_yes_QW_2 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_yes_Q_2 * BBW )
M222_3_1 <- sum((AA_no_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_2 ) * BB_no )
M222_3_2 <- sum((AA_yes_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_2 ) * BB_no)
M222_3_3 <- sum((AA_no_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_no_Q_3 * BBW )
M222_3_4 <- sum((AA_no_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_2 ) * BB_no)
M222_3_5 <- sum((AA_yes_PW_2 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_no_Q_3 * BBW )
M222_3_6 <- sum((AA_yes_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_2 ) * BB_no)
M222_3_7 <- sum((AA_no_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_yes_Q_3 * BBW )
M222_3_8 <- sum((AA_yes_PW_2 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_yes_Q_3 * BBW )
M222_4_1 <- sum((AA_no_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3 ) * BB_no )
M222_4_2 <- sum((AA_yes_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3 ) * BB_no)
M222_4_3 <- sum((AA_no_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_no_Q_3 * BBW )
M222_4_4 <- sum((AA_no_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3 ) * BB_no)
M222_4_5 <- sum((AA_yes_PW_3 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_no_Q_3 * BBW )
M222_4_6 <- sum((AA_yes_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3 ) * BB_no)
M222_4_7 <- sum((AA_no_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_yes_Q_3 * BBW )
M222_4_8 <- sum((AA_yes_PW_3 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_yes_Q_3 * BBW )
M222_5_1 <- sum((AA_no_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_4 ) * BB_no )
M222_5_2 <- sum((AA_yes_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_4 ) * BB_no)
M222_5_3 <- sum((AA_no_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_no_Q_3 * BBW )
M222_5_4 <- sum((AA_no_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_4 ) * BB_no)
M222_5_5 <- sum((AA_yes_PW_4 * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_no_Q_3 * BBW )
M222_5_6 <- sum((AA_yes_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_4 ) * BB_no)
M222_5_7 <- sum((AA_no_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_yes_Q_3 * BBW )
M222_5_8 <- sum((AA_yes_PW_4 * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_yes_Q_3 * BBW )
M222_6_1 <- mat_tri((AA_no_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_2 ) * BB_no )
M222_6_2 <- mat_tri((AA_yes_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_2 ) * BB_no)
M222_6_3 <- mat_tri((AA_no_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_no_Q_4 * BBW )
M222_6_4 <- mat_tri((AA_no_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_2 ) * BB_no)
M222_6_5 <- mat_tri((AA_yes_PW_2 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_no_Q_4 * BBW )
M222_6_6 <- mat_tri((AA_yes_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_2 ) * BB_no)
M222_6_7 <- mat_tri((AA_no_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_2) * BB_two + AA_no_P_2 * CC_yes_Q_4 * BBW )
M222_6_8 <- mat_tri((AA_yes_PW_2 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_2) * BB_two + AA_yes_P_2 * CC_yes_Q_4 * BBW )
M222_7_1 <- sum((AA_no_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_3 ) * BB_no )
M222_7_2 <- sum((AA_yes_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_3 ) * BB_no)
M222_7_3 <- sum((AA_no_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_no_Q_4 * BBW )
M222_7_4 <- sum((AA_no_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_3 ) * BB_no)
M222_7_5 <- sum((AA_yes_PW_3 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_no_Q_4 * BBW )
M222_7_6 <- sum((AA_yes_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_3 ) * BB_no)
M222_7_7 <- sum((AA_no_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_3) * BB_two + AA_no_P_3 * CC_yes_Q_4 * BBW )
M222_7_8 <- sum((AA_yes_PW_3 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_3) * BB_two + AA_yes_P_3 * CC_yes_Q_4 * BBW )
M222_8_1 <- mat_tri((AA_no_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_4 ) * BB_no )
M222_8_2 <- mat_tri((AA_yes_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_4 ) * BB_no)
M222_8_3 <- mat_tri((AA_no_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_no_Q_4 * BBW )
M222_8_4 <- mat_tri((AA_no_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_4 ) * BB_no)
M222_8_5 <- mat_tri((AA_yes_PW_4 * CC_no_Q_4 + CC_no_QW_4 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_no_Q_4 * BBW )
M222_8_6 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_4 ) * BB_no)
M222_8_7 <- mat_tri((AA_no_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_no_P_4) * BB_two + AA_no_P_4 * CC_yes_Q_4 * BBW )
M222_8_8 <- mat_tri((AA_yes_PW_4 * CC_yes_Q_4 + CC_yes_QW_4 *AA_yes_P_4) * BB_two + AA_yes_P_4 * CC_yes_Q_4 * BBW )
M222_9_1 <- sum((AA_no_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3t ) * BB_no )
M222_9_2 <- sum((AA_yes_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3t ) * BB_no)
M222_9_3 <- sum((AA_no_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_no_P_3t) * BB_two + AA_no_P_3t * CC_no_Q_3 * BBW )
M222_9_4 <- sum((AA_no_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3t ) * BB_no)
M222_9_5 <- sum((AA_yes_PW_3t * CC_no_Q_3 + CC_no_QW_3 *AA_yes_P_3t) * BB_two + AA_yes_P_3t * CC_no_Q_3 * BBW )
M222_9_6 <- sum((AA_yes_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3t ) * BB_no)
M222_9_7 <- sum((AA_no_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_no_P_3t) * BB_two + AA_no_P_3t * CC_yes_Q_3 * BBW )
M222_9_8 <- sum((AA_yes_PW_3t * CC_yes_Q_3 + CC_yes_QW_3 *AA_yes_P_3t) * BB_two + AA_yes_P_3t * CC_yes_Q_3 * BBW )
motif_weighted <- c(M111,M112_1,M112_2,M211_1,M211_2,M212_1,M212_2,M212_3,M212_4,M121_1,M121_2,M122_1_1,M122_1_2,M122_1_3,M122_1_4,
M122_2_1,M122_2_2,M122_2_3,M122_2_4,M122_3_1,M122_3_2,M122_3_3,M122_3_4,M221_1_1,M221_1_2,M221_1_3,M221_1_4,
M221_2_1,M221_2_2,M221_2_3,M221_2_4,M221_3_1,M221_3_2,M221_3_3,M221_3_4,M222_1_1,M222_1_2,M222_1_3,M222_1_4,
M222_1_5,M222_1_6,M222_1_7,M222_1_8,M222_2_1,M222_2_2,M222_2_3,M222_2_4,M222_2_5,M222_2_6,M222_2_7,M222_2_8,
M222_3_1,M222_3_2,M222_3_3,M222_3_4,M222_3_5,M222_3_6,M222_3_7,M222_3_8,
M222_4_1,M222_4_2,M222_4_3,M222_4_4,M222_4_5,M222_4_6,M222_4_7,M222_4_8,
M222_5_1,M222_5_2,M222_5_3,M222_5_4,M222_5_5,M222_5_6,M222_5_7,M222_5_8,
M222_6_1,M222_6_2,M222_6_3,M222_6_4,M222_6_5,M222_6_6,M222_6_7,M222_6_8,
M222_7_1,M222_7_2,M222_7_3,M222_7_4,M222_7_5,M222_7_6,M222_7_7,M222_7_8,
M222_8_1,M222_8_2,M222_8_3,M222_8_4,M222_8_5,M222_8_6,M222_8_7,M222_8_8,
M222_9_1,M222_9_2,M222_9_3,M222_9_4,M222_9_5,M222_9_6,M222_9_7,M222_9_8)
intra_guild_edge <- c(2, 3, 4, 3, 4, 4, 5, 5, 6, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7,
8, 5, 6, 6, 6, 7, 7, 7, 8, 6, 7, 7, 7, 8, 8, 8, 9, 5, 6, 6, 6, 7, 7, 7, 8, 6, 7, 7, 7, 8, 8, 8, 9, 7, 8, 8, 8, 9, 9, 9,
10, 6, 7, 7, 7, 8, 8, 8, 9, 7, 8, 8, 8, 9, 9, 9, 10, 8, 9, 9, 9, 10, 10, 10, 11, 6, 7, 7, 7, 8, 8, 8, 9)
mean_weighted <- motif_weighted/(intra_guild_motif * intra_guild_edge)
mean_weighted <- replace(mean_weighted,which(is.nan(mean_weighted)),NA)
names(mean_weighted)<-motif_names
return(list(intra_guild_icmotif=intra_guild_motif,mean_weight=mean_weighted))
}
else{
names(intra_guild_motif)<-motif_names
return(intra_guild_motif)
}
}
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