What is the primary function of active edges in a directed network?

Active edges in a directed network play a crucial role in maintaining the flow of activities. In a directed network, which can represent various systems such as project management (like PERT and CPM), transportation systems, or information flow, active edges indicate pathways through which tasks or activities are currently being executed or processed. This means that the edges or connections between nodes (which represent tasks or activities in this context) enable the movement or flow of information, resources, or activities through the network.

By actively maintaining the connections that represent ongoing processes, these edges help reflect the state of the network at any given moment. In project management, for instance, active edges would correspond to tasks that are currently in progress, highlighting how activities are dependent on one another and how they interact. Understanding which edges are active allows for better planning and optimization of workflows, making it easier to identify bottlenecks or inefficiencies within the system.