The degree of a vertex in a graph refers to the number of edges connected to that vertex. Here's how you can determine it:

1. Identify the Vertex: Select the vertex for which you want to find the degree.

2. Count the Edges: Count all the edges that are connected to the vertex. If the graph is undirected, each edge is counted as 1. If the graph is directed, count:

   • In-degree: Number of edges coming into the vertex.
   • Out-degree: Number of edges going out from the vertex.

3. Account for Loops: If there is a loop (an edge connecting a vertex to itself), count it twice for the degree because it contributes to both in-degree and out-degree.

4. Add the Connections: Sum up the edges connected to the vertex to find its degree.

Example

In the following graph:

  A ----- B
   \     /
    C   D

• Degree of A = 2 (edges to B and C)
• Degree of B = 2 (edges to A and D)
• Degree of C = 1 (edge to A)
• Degree of D = 1 (edge to B)

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Would you like further details or examples? Here are 5 questions to deepen your understanding:

1. How does the degree of a vertex differ between directed and undirected graphs?
2. What is the sum of the degrees of all vertices in an undirected graph?
3. Can a vertex have a degree of 0? What does this signify?
4. How do loops impact the degree of a vertex in a directed graph?
5. How can we use degree to classify vertices into isolated, pendant, or regular?

Tip: The sum of degrees of all vertices in an undirected graph is always twice the total number of edges.