B1I | R Documentation |

This function calculates the `B1`

index `B1(T)`

for a given rooted
tree `T`

. The tree must not necessarily be binary. `B1(T)`

is defined as

`B1(T)=\sum_{u\in V_{in}(T)\setminus\{\rho\}} h(T_u)^{-1}`

in which
`V_{in}(T)\setminus\{\rho\}`

denotes the set of inner vertices of `T`

without the root, and
`h(T_u)`

denotes the height of the pending subtree rooted at `u`

.
When restricted to binary trees, the `B1`

index is a balance index. For
arbitrary trees it does not fulfill the definition of an (im)balance index.

For `n=1`

the function returns `B1(T)=0`

and a warning.

For details on the B1 index, see
also Chapter 10 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_10).

```
B1I(tree)
```

`tree` |
A rooted tree in phylo format. |

`B1I`

returns the B1 index of the given tree.

Sophie Kersting

K.-T. Shao and R. R. Sokal. Tree Balance. Systematic Zoology, 39(3):266, 1990.

doi: 10.2307/2992186.

```
tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
B1I(tree)
```

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