1. Level 1
height
Level 2
width
Height = 2, 2 levels
Width = 4
Shallow tree
height
width
Height = 5, 5 levels
Max width = 2
Deep tree

2. Level 1 breadth = 5
Depth = 3
Maximum breadth = max{5, 4, 3} = 5

3. Depth = 5. This is NOT the breadth of the menu tree.
Level 1 breadth = 5
Level 2 breadth = 3
Depth = 5. This is NOT the breadth of the menu tree.
Maximum breadth = max{5, 3, 3, 5, 3} = 5
Mean breadth = 3.8

4. The menu tree here has two levels, depth = 2
The menu tree here has two levels, depth = 2. But the maximum breadth = 35
Level 1 breadth = 9
35 options
This is a shallow tree.

5. Example of structuring a menu level with many items without increasing the depth

6. Summary Depth = # of levels
Breadth = Can be described as average items per level or as maximum items per level.
Further reading:
Flat vs. Deep Website Hierarchies
The depth/breadth trade-off in the design of menu-driven user interfaces
Hierarchical Menu Design: Breadth, Depth, and Task Complexity
More…
Depth vs. Breadth of Hierarchical Menu Trees
Web navigation structures in cellular phones: the depth/breadth trade-off issue