C++ - BFS and a Directed Graph / Adjacency List

I'm trying to wrap my head around a breadth first search on a directed graph with an array of vertices and an adjacency list.

For example:
[1]->null
[2]->[1]
[3]->[2]->[1]
[4]->[3]

I understand that the BFS visits children before proceeding to grandchildren (or whatever language you want to use).

But if the vertices themselves are not necessarily linked, would the BFS just be performed on each individual vertex? And wouldn't it just be displaying them in their adjacency list order?

Let me know if you have any advice or tips.
¿what's confusing you?
¿do you understand bfs on an empty graph? ¿or with just one vertex?

¿what's so different with a directed graph?
No, I don't understand BFS with just one vertex. It seems like it would just be displaying them in order.
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