Two classes can only provide a bare introduction to this area. The points I would like you to take away are:
1) Networks are an important subclass of linear programs that are intuitive, easy to solve, and have nice integrality properties.
2) Problems that might not look like networks might be networks.
3) Networks provide a useful way to think about problems even if there are additional constraints or variables that preclude use of networks for modeling the whole problem.
In practice, you would generally save using the fastest network codes until the final implementation phase. Until then, linear programming codes will tend to be sufficiently fast to prove the concepts.