What is the least number of edges needed to connect a directed graph starting from the root?

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It depends on the specific graph and its structure. In general, the minimum number of edges needed to connect a directed graph starting from the root would be the number of edges in the longest path from the root to any leaf node. This is commonly referred to as the "depth" of the graph. However, some graphs may have multiple paths of equal length, in which case the minimum number of edges needed to connect the graph would be the number of edges in any one of those paths.