#' @title Quantification of (indirect) relations

#' @description Function to aggregate positions defined via indirect relations to construct centrality

#' scores.

#' @param tau_x Numeric matrix containing indirect relations calculated with [indirect_relations].

#' @param 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'.

#' @return Scores for the index defined by the indirect relation `tau_x` and the 

#' used aggregation type.

#' @author David Schoch

#' @seealso [indirect_relations], [transform_relations]

#' @examples

#' library(igraph)

#' library(magrittr)

#' 

#' g <- graph.empty(n=11,directed = FALSE)

#' g <- add_edges(g,c(1,11,2,4,3,5,3,11,4,8,5,9,5,11,6,7,6,8,

#'                    6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))

#'#degree

#' g %>% indirect_relations(type='adjacency') %>% 

#'  aggregate_positions(type='sum')

#'

#' #closeness centrality

#' g %>% indirect_relations(type='dist_sp') %>% 

#'   aggregate_positions(type='invsum')

#'   

#' #betweenness centrality

#' g %>% indirect_relations(type='depend_sp') %>% 

#'   aggregate_positions(type='sum')

#'   

#' #eigenvector centrality

#' g %>% indirect_relations(type='walks',FUN=walks_limit_prop) %>% 

#'   aggregate_positions(type='sum')

#'

#'#subgraph centrality

#' g %>% indirect_relations(type='walks',FUN=walks_exp) %>% 

#'   aggregate_positions(type='self')

#'   

#' @export

aggregate_positions <- function(tau_x, type = "sum") {

    } else {

    }

}