The degree of a vertex in a graph is determined by the number of edges that are directly connected to it. In the provided image, we are analyzing vertex $G$. To calculate the degree of $G$:

1. Count all edges connected to $G$:

   • Visually inspect and count all lines (edges) emanating from $G$.

2. Verify completeness:

   • Ensure all other vertices $A, B, C, D, E, F$ are connected to $G$.

The graph appears to be a complete graph, where each vertex is connected to every other vertex. In a complete graph with $n$ vertices, each vertex has a degree of $n-1$.

Here, the graph has $7$ vertices ($A, B, C, D, E, F, G$), so the degree of $G$ is: $\text{Degree of } G = 7 - 1 = 6$

The degree of vertex $G$ is 6.

Would you like me to expand on this explanation or provide additional details?

Related Questions:

1. How is the degree of a vertex calculated in different types of graphs (e.g., directed, undirected)?
2. What are the properties of a complete graph in terms of edges and degrees?
3. Can you explain the difference between degree, in-degree, and out-degree in directed graphs?
4. How does the concept of degree help in analyzing the connectivity of a graph?
5. How does the number of edges in a complete graph relate to the number of vertices?

Tip: In a complete graph, every vertex connects to every other vertex, simplifying the calculation of degrees.