Saturated Edge

http://www.cs.emory.edu/~cheung/Courses/253/Syllabus/NetFlow/intro.html

Saturated Edge:

• Definition: An edge is termed "saturated" if the flow through the edge is equal to the capacity of the edge. This is represented mathematically as:
  f(e)=c(e)
  Where:
  • f(e) is the flow through edge e
  • c(e) is the capacity of edge e

From the provided example:

• The edges in the flow network are labeled with two numbers: the first number indicates the flow through the edge, and the second number indicates the capacity of the edge.
• A saturated edge is indicated with a red arrow in the diagram.

Looking at the example, we can see the edge connecting node S to node B (S->B) and node E to node T (E->T) is labeled "2,2". The flow through this edge is 2, and its capacity is also 2. Since the flow equals the capacity, the edge is saturated, as indicated by its red color.

In summary, a saturated edge in a flow network is an edge where the current flow through it has reached its maximum allowable capacity. In the given image, this is visually represented by the red arrowed line between nodes S and B and nodes E and T.