## 3.1 Trees and Spanning Trees

Note: if you cannot remember what cycles or loops are, revise notes for 2.1 Introduction to Walks

### Trees

- A
**tree**is a**connected network graph**which**does not**contain loops, multiple edges or cycles. - One way of thinking about this, is that it is a graph that continuously branches out like a tree.
- Every connected graph will have at least one subgraph which is a tree.
- It uses the
**smallest**number of edges to connect the graph. - A tree with
**n vertices**has**n-1 edges**.

Example

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