# cophenetic

##### Cophenetic Distances for a Hierarchical Clustering

Computes the cophenetic distances for a hierarchical clustering.

- Keywords
- multivariate, cluster

##### Usage

```
cophenetic(x)
# S3 method for default
cophenetic(x)
# S3 method for dendrogram
cophenetic(x)
```

##### Arguments

##### Details

The cophenetic distance between two observations that have been clustered is defined to be the intergroup dissimilarity at which the two observations are first combined into a single cluster. Note that this distance has many ties and restrictions.

It can be argued that a dendrogram is an appropriate summary of some data if the correlation between the original distances and the cophenetic distances is high. Otherwise, it should simply be viewed as the description of the output of the clustering algorithm.

`cophenetic`

is a generic function. Support for classes which
represent hierarchical clusterings (total indexed hierarchies) can be
added by providing an `as.hclust()`

or, more directly, a
`cophenetic()`

method for such a class.

The method for objects of class `"dendrogram"`

requires
that all leaves of the dendrogram object have non-null labels.

##### Value

An object of class `"dist"`

.

##### References

Sneath, P.H.A. and Sokal, R.R. (1973)
*Numerical Taxonomy: The Principles and Practice of Numerical
Classification*, p.278 ff;
Freeman, San Francisco.

##### See Also

##### Examples

`library(stats)`

```
# NOT RUN {
require(graphics)
d1 <- dist(USArrests)
hc <- hclust(d1, "ave")
d2 <- cophenetic(hc)
cor(d1, d2) # 0.7659
## Example from Sneath & Sokal, Fig. 5-29, p.279
d0 <- c(1,3.8,4.4,5.1, 4,4.2,5, 2.6,5.3, 5.4)
attributes(d0) <- list(Size = 5, diag = TRUE)
class(d0) <- "dist"
names(d0) <- letters[1:5]
d0
utils::str(upgma <- hclust(d0, method = "average"))
plot(upgma, hang = -1)
#
(d.coph <- cophenetic(upgma))
cor(d0, d.coph) # 0.9911
# }
```

*Documentation reproduced from package stats, version 3.6.0, License: Part of R 3.6.0*