Counts the number of concordant, discordant and (left/right) ties between two rankings.

## Value

A list containing

- concordant
number of concordant pairs:

`x[i]`

>`x[j]`

and`y[i]`

>`y[j]`

- discordant
number of discordant pairs:

`x[i]`

>`x[j]`

and`y[i]`

<`y[j]`

- ties
number of tied pairs:

`x[i]`

==`x[j]`

and`y[i]`

==`y[j]`

- left
number of left ties:

`x[i]`

==`x[j]`

and`y[i]`

!=`y[j]`

- right
number of right ties:

`x[i]`

!=`x[j]`

and`y[i]`

==`y[j]`

## Details

Explicitly calculating the number of occurring cases is more robust
than using correlation indices as given in the `cor`

function. Especially
left and right ties can significantly alter correlations.

## Examples

```
library(igraph)
tg <- threshold_graph(100, 0.2)
compare_ranks(degree(tg), closeness(tg)) # only concordant pairs
#> $concordant
#> [1] 4654
#>
#> $discordant
#> [1] 0
#>
#> $ties
#> [1] 296
#>
#> $left
#> [1] 0
#>
#> $right
#> [1] 0
#>
compare_ranks(degree(tg), betweenness(tg)) # no discordant pairs
#> $concordant
#> [1] 1788
#>
#> $discordant
#> [1] 0
#>
#> $ties
#> [1] 296
#>
#> $left
#> [1] 0
#>
#> $right
#> [1] 2866
#>
## Rank Correlation
cor(degree(tg), closeness(tg), method = "kendall") # 1
#> [1] 1
cor(degree(tg), betweenness(tg), method = "kendall") # not 1, although no discordant pairs
#> [1] 0.6198271
```