Which of the following best describes the activity shown on a weighted edge?

The best description of the activity shown on a weighted edge is that it represents the time taken for the activity. In project management and network diagrams, edges (or arcs) with weights typically indicate the duration required to complete a specific task or activity. This means that each edge in the graphical representation has a numerical value associated with it that reflects how long that particular activity will take.

Understanding the weighted edge as the time taken for the activity is key in project planning since it allows for efficient scheduling and resource allocation. Knowing how long each activity will take helps in determining the overall project timeline and in identifying critical paths. This ensures that project managers can effectively manage resources and adhere to deadlines.

The other options do not accurately reflect what a weighted edge conveys in this context. For instance, while the total duration of the project involves considering all activities, it is not what is directly shown by a single weighted edge. The importance of an activity or the percentage of completion are also more abstract concepts and do not indicate the specific time required for the task, which is the primary focus of a weighted edge in this scenario.