Function to aggregate positions defined via indirect relations to construct centrality scores.

## Arguments

- tau_x
Numeric matrix containing indirect relations calculated with indirect_relations.

- type
String indicating the type of aggregation to be used. See Details for options.

## Details

The predefined functions are mainly wrappers around base R functions.
type='sum', for instance, is equivalent to `rowSums()`

. A non-base functions is
type='invsum' which calculates the inverse of type='sum'.
type='self' is mostly useful for walk based relations, e.g. to count closed walks.
Other self explanatory options are type='mean', type='min', type='max' and type='prod'.

## Examples

```
library(igraph)
#>
#> Attaching package: ‘igraph’
#> The following objects are masked from ‘package:stats’:
#>
#> decompose, spectrum
#> The following object is masked from ‘package:base’:
#>
#> union
library(magrittr)
data("dbces11")
# degree
dbces11 %>%
indirect_relations(type = "adjacency") %>%
aggregate_positions(type = "sum")
#> A B C D E F G H I J K
#> 1 1 2 2 3 4 4 4 4 4 5
# closeness centrality
dbces11 %>%
indirect_relations(type = "dist_sp") %>%
aggregate_positions(type = "invsum")
#> A B C D E F G
#> 0.03703704 0.02941176 0.04000000 0.04000000 0.05000000 0.05882353 0.05263158
#> H I J K
#> 0.05555556 0.05555556 0.05263158 0.05555556
# betweenness centrality
dbces11 %>%
indirect_relations(type = "depend_sp") %>%
aggregate_positions(type = "sum")
#> A B C D E F G H
#> 0.000000 0.000000 0.000000 18.000000 7.666667 19.666667 5.333333 32.666667
#> I J K
#> 14.666667 2.666667 29.333333
# eigenvector centrality
dbces11 %>%
indirect_relations(type = "walks", FUN = walks_limit_prop) %>%
aggregate_positions(type = "sum")
#> A B C D E F G H
#> 0.2751607 0.0786437 0.4610603 0.2941027 0.6952060 1.1990379 1.2177246 1.0212076
#> I J K
#> 1.1097768 1.2160775 1.0290143
# subgraph centrality
dbces11 %>%
indirect_relations(type = "walks", FUN = walks_exp) %>%
aggregate_positions(type = "self")
#> A B C D E F G H
#> 1.825100 1.595400 3.148571 2.423091 4.387127 7.807257 7.939410 6.672783
#> I J K
#> 7.032672 8.242124 7.389559
```