I want to calculate a formula in R - r

Question

I have a dataset that starts like this:
In dput it is
structure(list(20, TRUE, c(0, 0, 1, 1, 1, 1, 2, 3, 4, 4, 4, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7), c(8, 1, 0, 8, 9, 5,
8, 10, 10, 5, 7, 4, 11, 12, 6, 13, 14, 15, 16, 17, 18, 4, 5,
19, 4, 17), c(1, 0, 2, 5, 3, 4, 6, 7, 9, 10, 8, 11, 14, 12, 13,
15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25), c(2, 1, 11, 21,
24, 5, 9, 22, 14, 10, 0, 3, 6, 4, 7, 8, 12, 13, 15, 16, 17, 18,
19, 25, 20, 23), c(0, 2, 6, 7, 8, 11, 21, 24, 26, 26, 26, 26,
26, 26, 26, 26, 26, 26, 26, 26, 26), c(0, 1, 2, 2, 2, 5, 8, 9,
10, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26), list(c(1,
0, 1), structure(list(), names = character(0)), list(name = c("1",
"3", "5", "6", "8", "9", "12", "19", "2", "4", "7", "10", "11",
"14", "15", "16", "17", "18", "20", "13")), list(`Number of messages` = c(157,
1058, 2481, 833, 178, 119, 66, 222, 20, 343, 3, 4991, 47, 11,
83, 26, 10, 19, 33, 84, 51, 589, 79, 37, 110, 55))), <environment>), class = "igraph")
so far I have the following codelines:
Datensatz <- read_xlsx("...")
Netzwerkgraph <- graph.data.frame(Datensatz[,1:3], directed = TRUE)
actors<-Datensatz$From
relations<-Datensatz$To
weight<-Datensatz$`Number of messages`
How can I calculate the following formula in R with my data set?
I´ve tried the following code
Function <- function(i,j,x,y,z){
i <- actors
j <- relations
w <- weight
for(i in 1:20)
print (-1/(cumsum 1:length(actors, i)(w,i+1))logb(x,base=2)*1/(cumsum 1:length(actors, i)*w,i+1))
}

Answer 1

It isn't entirely clear how you wish to apply the given formula to your example data set, that is, exactly what inputs you are using and what outputs you wish to achieve. Hence, it also isn't clear if the following approach will be sufficient for your purposes. Here is my interpretation thus far.
If one interprets each unique value in the "from" column as being a node i, then it appears that you wish to calculate the sum of messages to each j in the "to" column for each sender i in the "from" column. One approach might then be to calculate all such sums by sender first and then run them all through a simple function that accepts the sum along with some lambda constant.
I used a lambda value of "2" below arbitrarily for illustrative purposes. Additionally, while the formula references a time t, there does not appear to be a time component in your example data set; time isn't represented in this approach. The output would presumably represent the expression for each node at a single point in time.
#written in R version 4.2.1
require(data.table)
##Example data frame
df = data.frame(from = c(1,1,3,3,3), to = c(2,3,1,2,4),nm = c(157,1058,2481,833,178))
df = data.table(df)
df
from to nm
1: 1 2 157
2: 1 3 1058
3: 3 1 2481
4: 3 2 833
5: 3 4 178
##Calculate the sum of messages by sender in "from" column
nf = df[,sum(nm), by = from]
colnames(nf) = c("from","message_total")
nf
from message_total
1: 1 1215
2: 3 3492
## Function
## inputs to function are the total number of messages of a sender in
## "from" column (called cit) and some lambda constant
icit = function(cit,lambda = 2){
-(1/(cit + lambda))*log(1/((cit + lambda)), base = 2)
}
##Find vector of values for each sender in the data set
ans = NULL
for(i in 1:dim(nf)[1]){
ans[i] = icit(nf$message_total[i])
}
ans
[1] 0.008421622 0.003368822