Regarding "type 2" graphs: What is the exact constrain on the capacity of the edges?
For instance, let's take a flow network which holds the following:
1. All vertices (except s and t) have in degree <=1 or out degree <=1
2. All outgoing edges from s has a capacity of 2 (these are all the edges directed to one group of vertices, one edge for each vertex), and all incoming edges of t has a capacity of 2 (these are all the edges directed from the second group of vertices, one edge from each vertex)
Is this network considered a type-2 network, with the same Dinic complexity? Is it possible to use any other constant instead of 2, as long as all the "inner" edges between the two groups of vertices has a capacity of 1?