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This problem asks about a complete undirected graph with five vertices. In a **complete graph**, every vertex is connected to every other vertex by an edge.

### Step-by-step solution:
1. **Vertices (n):** There are 5 vertices in this graph.
2. **Edges:** In a complete graph, the number of edges is given by the formula:
   \[
   \text{Number of edges} = \frac{n(n - 1)}{2}
   \]
   where \( n \) is the number of vertices.

3. **Substitute \( n = 5 \):**
   \[
   \text{Number of edges} = \frac{5(5 - 1)}{2} = \frac{5 \times 4}{2} = 10
   \]

Thus, the complete graph on five vertices has **10 edges**.

Would you like a detailed explanation of any part of this problem? 

Here are 5 related questions to further explore the topic:
1. What is the general structure of a complete graph with \( n \) vertices?
2. How many edges would a complete graph with 6 vertices have?
3. How do you differentiate between a complete graph and other types of graphs?
4. Can a directed graph also be complete, and how would the edge count differ?
5. What are real-world examples of applications of complete graphs in networks?

### Tip:
In graph theory, the complete graph on \( n \) vertices is often denoted by \( K_n \), where \( n \) represents the number of vertices.

An undirected graph is called complete if every vertex shares an edge with every other vertex. Draw a complete graph on five vertices. How many edges does it have?

Learn how to calculate the number of edges in a complete graph with 5 vertices. Understand graph theory concepts and the formula n(n - 1) / 2 for determining the number of edges. Suitable for high school students studying combinatorics and graph theory.

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