In Out Degree Edc921

1. **Stating the problem:** We want to understand how to identify the in-degree and out-degree of a vertex in a directed graph. 2. **Definitions:** - The **in-degree** of a vertex is the number of edges coming *into* that vertex. - The **out-degree** of a vertex is the number of edges going *out* from that vertex. 3. **Formula:** - If $v$ is a vertex, then: - $$\text{in-degree}(v) = \text{number of edges with } v \text{ as the target}$$ - $$\text{out-degree}(v) = \text{number of edges with } v \text{ as the source}$$ 4. **How to identify:** - Look at all edges connected to the vertex. - Count how many edges point towards the vertex (in-degree). - Count how many edges start from the vertex (out-degree). 5. **Example:** - If vertex $A$ has 3 edges coming in and 2 edges going out, then: - $$\text{in-degree}(A) = 3$$ - $$\text{out-degree}(A) = 2$$ 6. **Summary:** - In-degree counts incoming edges. - Out-degree counts outgoing edges. - This helps analyze flow or connectivity in directed graphs.