To determine the number of edges in the graph, let's count the edges directly from the image.

1. Start from the central node and count the edges radiating outwards.
2. Move to each surrounding node and count the edges connecting to other nodes.

Let's label the nodes for clarity:

• Central node: $A$
• Surrounding nodes: $B, C, D, E, F, G$

Now, count the edges:

1. From $A$:

   • $A$ to $B$
   • $A$ to $C$
   • $A$ to $D$
   • $A$ to $E$
   • $A$ to $F$
   • $A$ to $G$

   Total edges from $A$: 6

2. From each surrounding node to other surrounding nodes:

   • $B$ to $C, D, E, F$ (4 edges)
   • $C$ to $B, D, E, G$ (excluding $B$): 3 edges
   • $D$ to $B, C, E, F$ (excluding $B, C$): 2 edges
   • $E$ to $B, C, D, F$ (excluding $B, C, D$): 1 edge
   • $F$ to $B, D, E, G$ (excluding $B, D, E$): 1 edge
   • $G$ to $C, F$ (excluding $C, F$): 0 edges

Let's summarize:

• Total edges radiating from $A$: 6
• Total additional edges between surrounding nodes: $4 + 3 + 2 + 1 + 1 = 11$

Thus, the total number of edges in the graph is:

$6 + 11 = 17$

However, it's important to validate by checking each pair to ensure no double-counting.

• Double-check central connections: 6
• Double-check surrounding connections:
  • $B$ to $C, D, E, F$: 4
  • $C$ to $D, E, G$: 3
  • $D$ to $E, F$: 2
  • $E$ to $F$: 1
  • $F$ to $G$: 1

Therefore, total is $6 + 11 = 17$.

The graph has 17 edges.

Would you like more details or have any questions? Here are some questions you might want to explore:

1. How do you determine the degree of a node in a graph?
2. What are different types of graphs in graph theory?
3. How can you represent this graph using an adjacency matrix?
4. What is the significance of the Euler characteristic in graph theory?
5. How would you identify if this graph is bipartite?

Tip: In graph theory, always verify your edge counts to avoid double-counting or missing any connections.