To find a minimum spanning tree (MST) for a graph, the number of edges in the MST is determined by the number of nodes in the graph. Specifically, for a graph with $n$ nodes, the number of edges in any MST is always $n - 1$.

In your case, the graph $G$ has 9 nodes. Therefore, the number of edges that must be included in any minimal spanning tree of $G$ is:

$9 - 1 = 8$

Thus, any minimum spanning tree of this graph will have 8 edges.

Would you like further details or have any questions?

Here are some related questions for deeper exploration:

1. What is the difference between a minimum spanning tree and a shortest path tree?
2. How does Kruskal's algorithm find a minimum spanning tree?
3. How does Prim's algorithm differ from Kruskal's algorithm when finding an MST?
4. Can a graph have more than one minimum spanning tree? If so, under what conditions?
5. What is the time complexity of finding a minimum spanning tree using different algorithms?

Tip: When working with weighted graphs, ensure that all edge weights are distinct to guarantee a unique minimum spanning tree.