What is an 'Augmenting Path' in flow networks?

What is an 'Augmenting Path' in flow networks?

Approach: Define a path in the residual graph with available capacity.

A path from the source to the sink in the residual graph where every edge has a strictly positive residual capacity. Increasing flow along this path increases total network flow.

Follow-up: What happens when no augmenting paths exist?

Key concepts: residual graph, source/sink, bottleneck.