prestige {sna} | R Documentation

## Calculate the Vertex Prestige Scores

### Description

`prestige` takes one or more graphs (`dat`) and returns the prestige scores of positions (selected by `nodes`) within the graphs indicated by `g`. Depending on the specified mode, prestige based on any one of a number of different definitions will be returned. This function is compatible with `centralization`, and will return the theoretical maximum absolute deviation (from maximum) conditional on size (which is used by `centralization` to normalize the observed centralization score).

### Usage

    prestige(dat, g=1, nodes=NULL, gmode="digraph", diag=FALSE,
        cmode="indegree", tmaxdev=FALSE, rescale=FALSE, tol=1e-07)

### Arguments

`dat` | one or more input graphs.
`g` | integer indicating the index of the graph for which centralities are to be calculated (or a vector thereof). By default, `g==1`.
`nodes` | vector indicating which nodes are to be included in the calculation. By default, all nodes are included.
`gmode` | string indicating the type of graph being evaluated. "digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. `gmode` is set to "digraph" by default.
`diag` | boolean indicating whether or not the diagonal should be treated as valid data. Set this true if and only if the data can contain loops. `diag` is `FALSE` by default.
`cmode` | one of "indegree", "indegree.rownorm", "indegree.rowcolnorm", "eigenvector", "eigenvector.rownorm", "eigenvector.colnorm", "eigenvector.rowcolnorm", "domain", or "domain.proximity".
`tmaxdev` | boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, `tmaxdev==FALSE`.
`rescale` | if true, centrality scores are rescaled such that they sum to 1.
`tol` | Currently ignored

### Details

"Prestige" is the name collectively given to a range of centrality scores which focus on the extent to which one is nominated by others. The definitions supported here are as follows:

1. indegree: indegree centrality
2. indegree.rownorm: indegree within the row-normalized graph
3. indegree.rowcolnorm: indegree within the row-column normalized graph
4. eigenvector: eigenvector centrality within the transposed graph (i.e., incoming ties recursively determine prestige)
5. eigenvector.rownorm: eigenvector centrality within the transposed row-normalized graph
6. eigenvector.colnorm: eigenvector centrality within the transposed column-normalized graph
7. eigenvector.rowcolnorm: eigenvector centrality within the transposed row/column-normalized graph
8. domain: indegree within the reachability graph (Lin's unweighted measure)
9. domain.proximity: Lin's proximity-weighted domain prestige

Note that the centralization of prestige is simply the extent to which one actor has substantially greater prestige than others; the underlying definition is the same.

### Value

A vector, matrix, or list containing the prestige scores (depending on the number and size of the input graphs).

### Warning

Making adjacency matrices doubly stochastic (row-column normalization) is not guaranteed to work. In general, be wary of attempting to try normalizations on graphs with degenerate rows and columns.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

Lin, N. (1976). Foundations of Social Research. New York: McGraw Hill.

Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.

### See Also

`centralization`

### Examples

    g<-rgraph(10)                 #Draw a random graph with 10 members
    prestige(g,cmode="domain")    #Compute domain prestige scores

[Package sna version 1.1 Index]