What does the level graph in Dinic's algorithm represent?

Question

I understand what a residual graph is. But what does a level graph mean? http://en.wikipedia.org/wiki/Dinic%27s_algorithm

Answer 1

From the Wikipedia article, the level graph is the subgraph of the residual graph with edges

E_L = {(u, v) in E_f : dist(v) = dist(u) + 1},

where E_f is the set of edges in the residual graph, and dist(w) is the unweighted distance from the source s to w.

In English, E_L is comprised of the edges of the residual graph that belong to some unweighted shortest path from s.

Answer 2

In a level graph edges between two vertices have same distance label are not kept. In network flows we use BFS to find level graph.

We also delete vertices from where sink is not reachable and also which are not reachable from source.