How to convert an undirected graph to a DAG?

Question

The Wiki page says

Any undirected graph may be made into a DAG by choosing a total order for its vertices and orienting every edge from the earlier endpo

Answer 1

Actually I think what it means in the wiki page by "choosing a total order" means defining a total order yourself. In other words, if we check the simplest undirected graph:

A----B

Converting this undirected graph to a DAG clearly depends on whether you choose to order A before B or A after B. If you choose A before B, then it becomes:

A--->B

Otherwise, it becomes:

B--->A

That is exactly what it means by "orienting every edge" from the "EARLIER" endpoint (endpoints that appear earlier in the total order) to the "LATER" endpoint.

Similarly, for:

    A
   / \
  /   \
 B-----C

If you define the total order as:

B A C

Then the directed graph should be something like:

B->A, B->C, A->C