Fixing the First and Last Numbers in a Random List - r

Question

I used this code to generate these random numbers (corresponds to an edge list for a graph) such that (Generating Random Graphs According to Some Conditions):
The first and last "nodes" are the same (e.g. starts at "1" and ends at "1")
Each node is visited exactly once
See below:
d = 15
relations = data.frame(tibble(
from = sample(data$d),
to = lead(from, default=from[1]),
))
> relations
from to
1 1 11
2 11 7
3 7 5
4 5 10
5 10 13
6 13 9
7 9 15
8 15 2
9 2 3
10 3 4
11 4 8
12 8 6
13 6 12
14 12 14
15 14 1
If I re-run this above code, it will (naturally) produce a different list:
relations
from to
1 6 9
2 9 2
3 2 5
4 5 8
5 8 13
6 13 1
7 1 14
8 14 3
9 3 11
10 11 12
11 12 7
12 7 15
13 15 4
14 4 10
15 10 6
Can I do something so that each time I generate a new random set of numbers, I can fix the first and last number to a specific number?
For instance, could I make it so that the first number and the last number are always "7"?
#example 1
from to
1 7 11
2 11 1
3 1 5
4 5 10
5 10 13
6 13 9
7 9 15
8 15 2
9 2 3
10 3 4
11 4 8
12 8 6
13 6 12
14 12 14
15 14 7
#example 2
from to
1 7 9
2 9 2
3 2 5
4 5 8
5 8 13
6 13 1
7 1 14
8 14 3
9 3 11
10 11 12
11 12 6
12 6 15
13 15 4
14 4 10
15 10 7
In the above examples (example 1, example 2), I took the first two random lists I made and manually replaced the first number and last number with 7 - and then replaced the replacement numbers as well.
But is there a way to "automatically" do this instead of making a manual correction?
For example, I think I figured out how to do this:
#run twice to make sure the output is correct
relations = data.frame(tibble(
from = sample(data$d),
to = lead(from, default=from[1]),
))
orig_first = relations[1,1]
relations[1,1] = 7
relations[15,2] = 7
relation = relations[-c(1,15),]
r1 = relations[1,]
r2 = relations[15,]
final_relation = rbind(r1, relation, r2)
#output 1 : seems correct (starts with 7, ends with 7, all nodes visited exactly once)
from to
1 7 8
2 8 4
3 4 7
4 7 13
5 13 1
6 1 14
7 14 6
8 6 9
9 9 11
10 11 10
11 10 12
12 12 2
13 2 5
14 5 15
15 15 7
#output 2: looks correct
from to
1 7 9
2 9 2
3 2 1
4 1 6
5 6 3
6 3 10
7 10 11
8 11 14
9 14 12
10 12 7
11 7 13
12 13 4
13 4 15
14 15 8
15 8 7
Am I doing this correctly? Is there an easier way to do this?
Thank you!

Answer 1

Here is a way to do this -
library(dplyr)
set.seed(2021)
d = 15
fix_num <- 7
relations = tibble(
from = c(fix_num, sample(setdiff(1:d, fix_num))),
to = lead(from, default=from[1]),
)
relations
# A tibble: 15 x 2
# from to
# <dbl> <dbl>
# 1 7 8
# 2 8 6
# 3 6 11
# 4 11 15
# 5 15 4
# 6 4 14
# 7 14 9
# 8 9 10
# 9 10 3
#10 3 5
#11 5 12
#12 12 13
#13 13 1
#14 1 2
#15 2 7