Maximum bipartite matching: show equivalence to max flow in unit-capacity networks.

In a large social network, users can be divided into two groups: content creators and content consumers. To facilitate meaningful interactions, the platform wants to establish a maximum number of one-to-one connections between creators and consumers, ensuring that each creator is connected to at most one consumer and each consumer is connected to at most one creator. This problem can be modeled as a maximum bipartite matching problem, where the goal is to find the largest possible subset of connections such that no two connections share a common creator or consumer. Show that this problem is equivalent to finding the maximum flow in a unit-capacity network.

Examples
Input: "test_input_1"
Output: "output_1"
Hints

Maximum bipartite matching: show equivalence to max flow in unit-capacity networks.

In a large social network, users can be divided into two groups: content creators and content consumers. To facilitate meaningful interactions, the platform wants to establish a maximum number of one-to-one connections between creators and consumers, ensuring that each creator is connected to at most one consumer and each consumer is connected to at most one creator. This problem can be modeled as a maximum bipartite matching problem, where the goal is to find the largest possible subset of connections such that no two connections share a common creator or consumer. Show that this problem is equivalent to finding the maximum flow in a unit-capacity network.