Network Flow and Max-Flow Min-Cut
Maximum flow equals minimum cut capacity.
Key idea
Maximum flow equals minimum cut capacity.
In depth
A flow network sends flow from source to sink through edges with capacities. The maximum flow equals the capacity of the minimum cut. The Ford–Fulkerson method finds it by augmenting paths.
Worked example
If every cut separating source from sink has capacity at least 7 and one equals 7, max flow = 7.
Real-world uses
- Finding the maximum water or traffic that can pass through a pipe or road network
Common mistake
Forgetting to allow flow to be undone along residual edges.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Network Flow and Max-Flow Min-Cut?
Maximum flow equals minimum cut capacity. It is a topic at the expert level in Discrete Math & Number Theory.
Where is Network Flow and Max-Flow Min-Cut used in real life?
Real-world examples: Finding the maximum water or traffic that can pass through a pipe or road network.
What should I learn before Network Flow and Max-Flow Min-Cut?
Make sure you are comfortable with Bipartite Graphs and Matching, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Network Flow and Max-Flow Min-Cut?
Forgetting to allow flow to be undone along residual edges.
How can I practise Network Flow and Max-Flow Min-Cut?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Network Flow and Max-Flow Min-Cut?
Move on to Adjacency Matrices next.
Related expert topics in Discrete Math & Number Theory
- Strong Induction – Assume all earlier cases to prove the next.
- Well-Ordering Principle – Every nonempty set of positive integers has a least element.
- Partial Orders – Reflexive, antisymmetric, transitive relations.
- Cardinality of Sets – Comparing sizes of infinite sets.
- Countable and Uncountable Sets – ℕ and ℚ are countable; ℝ is not.
- Cantor’s Diagonal Argument – Proof that real numbers are uncountable.