The CLRS book states that the Relabel to Front algorithm, which solves the problem of maximum data flow, keeps a list of topologically sorted nodes in the allowed network and moves nodes with zero excess data flow to the top of the list.

I do not quite understand what that means. ~~I would imagine that the vertices are sorted by the number of allowed edges that fall on them~~, But how would moving vertices without excessive flow forward in this case affect the sort order? Why is it that the list is already sorted when initialized in random order of vertices?

**To edit:**

It has just been recognized that the topological sorting of vertices in the allowed network means that for each valid edge (u, v) in the allowed network, the vertex u in the list appears before v.

However, this does not answer the last two parts of my question, as it is that the list is already sorted at initialization and how moving vertices with zero overflow forward affects the order. Thank you very much.