Nothing
oneEdgeDeletedSubgraphComplexity <- function(g, one.eds=NULL) {
if (class(g)[1] != "graphNEL")
stop("'g' has to be a 'graphNEL' object")
stopifnot(.validateGraph(g))
if(numEdges(g)==0)
stop("No edges in current graph object")
#################################
if (is.null(one.eds))
one.eds <- edgeDeletedSubgraphs(g)
n <- numNodes(g)
count <- length(one.eds)
# number of spanning trees in g
lap <- laplaceMatrix(g)
nST_g <- det(lap[2:n, 2:n])
# number of spanning trees in each subgraph and
# eigenvalues of Laplacian and signless Laplacian of each subgraph
data <- lapply(one.eds, function(M_1e) {
diag_1e <- diag(rowSums(M_1e, na.rm = FALSE, dims = 1))
lap_1e <- diag_1e - M_1e
nST_1e <- det(lap_1e[2:n, 2:n])
EV_lap_1e <- as.double(eigen(lap_1e, only.values = TRUE)$values)
signless_lap_1e <- diag_1e + M_1e
EV_signless_lap_1e <- as.double(eigen(signless_lap_1e, only.values = TRUE)$values)
list(nST = nST_1e, EV_lap = EV_lap_1e, EV_signless_lap = EV_signless_lap_1e)
})
# number of subgraphs that are nonisomorphic in terms of
# different spanning trees and spectrum of Laplacian and signless Laplacian
sST <- 0
sSpec <- 0
for (k in 1:(count-1)) {
for (l in (k+1):count) {
if (data[[k]]$nST == data[[l]]$nST) {
sST <- sST + 1
break
}
}
for (l in (k+1):count) {
if (setequal(data[[k]]$EV_lap, data[[l]]$EV_lap) &&
setequal(data[[k]]$EV_signless_lap, data[[l]]$EV_signless_lap)) {
sSpec <- sSpec + 1
break
}
}
}
N_1eST <- count - sST
N_1eSpec <- count - sSpec
# one-edge-deleted subgraph and spectrum complexity
m_cu <- n^1.68 - 10
C_1eST <- (N_1eST - 1) / (m_cu - 1)
C_1eSpec <- (N_1eSpec - 1) / (m_cu - 1)
list(`C_1eST` = C_1eST, `C_1eSpec` = C_1eSpec)
}
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