What does index stand for near the vector?

Question

We have a vector:

$\mathbf{v}^{(0)} = (0, 0, ..., 1, ..., 0, 0)$

I can't understand what u stand for to the right of vector:

$\ (\mathbf{v}^{(0)})_u = \{$ 1 when u = s, 0 when u ≠ s

u is not defined in document, so I ask there

s stands for node in graph, (0) stands for timestep in breadth-first search.

Answer 1

The subscript enumerates the vector's components.