Question

I am reading on Directed Acyclic Graphs and I can not understand the idea of topological order by relabeling.
My understanding of the topological order in general is that we find an order for the vertices such that we move from the one with no input edges to the next on the path and so forth untill we finish with all the vertices in the DAG.
But I don’t get how relabeling helps. I mean what is the point of relabeling the vertices? Don’t we actually break the graph this way?
Could anyone please explain in plain terms with an example of its application please?

Answer 1

I can’t tell for sure without a reference, but relabeling in this context usually means changing the order of the verticies. This doesn’t mean changing the topology of the graph (the edges and the verticies), it means changing the sort order.

You can also think of it as generating a permutation matrix or vector for a graph. This creates the a graph isomorphic to the original, but where vertex 1,2,3…,n correspond to the sorted order