In a digraph, the sum of the in-degrees is equal to:A. The number of verticesB. The number of edgesC. Twice the number of verticesD. Twice the number of edges
Question
In a digraph, the sum of the in-degrees is equal to:A. The number of verticesB. The number of edgesC. Twice the number of verticesD. Twice the number of edges
Solution
The correct answer is B. The number of edges.
Here's why:
In a directed graph (or digraph), each edge has an initial vertex and a terminal vertex. The in-degree of a vertex is the number of edges for which that vertex is the terminal vertex.
If you sum the in-degrees of all vertices in the digraph, you're essentially counting all edges, because each edge contributes exactly 1 to the total sum of in-degrees (it increases the in-degree of its terminal vertex by 1).
Therefore, in a digraph, the sum of the in-degrees is equal to the number of edges.
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