Now, we should have 0,1,0,0,0 series for vertex incoming degree.
So Windows calc gives σ(n)=0.4 and σ(n-1)~=0.44721, so where does 0.1788854
come from ?

Reason, I am asking because, I have a large graph, where the average looks
quite alright but the std makes no sense, as going by the histogram, degree
values are quite a bit more distributed than the std would indicate.

Now, we should have 0,1,0,0,0 series for vertex incoming degree.
So Windows calc gives σ(n)=0.4 and σ(n-1)~=0.44721, so where does 0.1788854
come from ?

Again, 0.4 / sqrt(5) = 0.17888543819998318...

Reason, I am asking because, I have a large graph, where the average looks
quite alright but the std makes no sense, as going by the histogram, degree
values are quite a bit more distributed than the std would indicate.

If you want the deviation of the distribution to compare with the
histogram, just multiply by sqrt(N).

I had the same problem. This topic answered me what I wanted, but I have a
doubt: Why this calculation is more importante/often then just standard
deviation of the distribution?
It is just a curiosity because I never saw that measurement

I had the same problem. This topic answered me what I wanted, but I have a
doubt: Why this calculation is more importante/often then just standard
deviation of the distribution?

Because we want to express the uncertainty of the mean, not of the
distribution.

It is just a curiosity because I never saw that measurement