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I'm a new VASP user, especially for the band structure calculations. I see that KPOINTS files are different for the GO/SP calculations and band calculations.

For example in here it shows KPOINTS file as

k-points for bandstructure L-G-X-U K-G
 10
line
reciprocal
  0.50000  0.50000  0.50000    1
  0.00000  0.00000  0.00000    1

  0.00000  0.00000  0.00000    1
  0.00000  0.50000  0.50000    1

  0.00000  0.50000  0.50000    1
  0.25000  0.62500  0.62500    1

  0.37500  0.7500   0.37500    1
  0.00000  0.00000  0.00000    1

I totally understand the path but the thing confuses me is the 10. How does it choose this 10? In the first step (standard DFT run) it used following KPOINTS

4x4x4
 0
G
 4 4 4
 0 0 0

Does it basically took a value that close to sum of kpoints from first step? In other words, let's say I choose 12 12 4 kgrid for the first step. Do I need to put something like 25 for the following band calculation?

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The "10" indicates the number of $\mathbf{k}$-points that will be calculated along each path segment. For example, the first path segment from $(0.5,0.5,0.5)$ to $(0,0,0)$ will contain 10 points, and similarly for all other segments. You have $4$ line segments in your example, so you will end up with a total of $40$ $\mathbf{k}$-points.

As to its value, you can choose a larger value if you want a finer resolution in your band structure, or a smaller value for coarser resolution. What you need will depend on what quantity you are interested in.

You can read more details about the KPOINTS file here:

https://www.vasp.at/wiki/index.php/KPOINTS

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Supplement some information to @ProfM's answer. Just for the logic.

The first step with uniform k-mesh, such as

  4x4x4
  0
  G
  4 4 4
  0 0 0

is to perform a self-consistent calculation to obtain converged charge density and wavefunction. (It is not hard to understood that why the charge density must sample the whole Brillouin zone.)

The second step with a line-mode k-sampling, such as

k-points for bandstructure L-G-X-U K-G
10
line
reciprocal
0.50000  0.50000  0.50000    1
0.00000  0.00000  0.00000    1

0.00000  0.00000  0.00000    1
0.00000  0.50000  0.50000    1

0.00000  0.50000  0.50000    1
0.25000  0.62500  0.62500    1

0.37500  0.7500   0.37500    1
0.00000  0.00000  0.00000    1

is to print the eigenvalue along the symmetric k-path based on the converged charge density or wavefunction from your first step, which is a post-process compared to step I. You can think line-mode k-mesh just extracts some pivotal information from the uniform k-mesh.

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