Which of the following correctly describes Prim's Algorithm?

Prim's Algorithm is a greedy algorithm that is used to find a minimum spanning tree for a graph. The process begins with a single vertex and expands the tree by adding edges that connect the tree to the rest of the graph.

The key aspect of Prim's Algorithm is that it always selects the minimum weight edge that connects a vertex in the growing tree to a vertex outside the tree. This ensures that the total weight of the edges in the spanning tree is minimized. By choosing the minimum weight edge at each step, the algorithm efficiently builds the spanning tree while ensuring that it is connected and contains no cycles.

The other options misrepresent the core principle of the algorithm. For instance, starting with a random edge or a maximum weight edge would not support the goal of achieving a minimum spanning tree, which is the essence of Prim's Algorithm. Therefore, the correct choice emphasizes the importance of selecting the edge with the minimum weight to ensure the optimal solution is reached.