graphcent {sna} | R Documentation

## Compute the (Harary) Graph Centrality Scores of Network Positions

### Description

`graphcent` takes one or more graphs (`dat`) and returns the Harary graph centralities of positions (selected by `nodes`) within the graphs indicated by `g`. Depending on the specified mode, graph centrality on directed or undirected geodesics 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

    graphcent(dat, g=1, nodes=NULL, gmode="digraph", diag=FALSE,
        tmaxdev=FALSE, cmode="directed", geodist.precomp=NULL,
        rescale=FALSE)

### 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` | List 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.
`tmaxdev` | Boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, `tmaxdev==FALSE`.
`cmode` | String indicating the type of graph centrality being computed (directed or undirected geodesics).
`geodist.precomp` | A `geodist` object precomputed for the graph to be analyzed (optional)
`rescale` | If true, centrality scores are rescaled such that they sum to 1.

### Details

The Harary graph centrality of a vertex v is equal to 1/(max_u d(v,u)), where d(v,u) is the geodesic distance from v to u. Vertices with low graph centrality scores are likely to be near the ``edge'' of a graph, while those with high scores are likely to be near the ``middle.'' Compare this with `closeness`, which is based on the reciprocal of the sum of distances to all other vertices (rather than simply the maximum).

### Value

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

### Note

Judicious use of `geodist.precomp` can save a great deal of time when computing multiple path-based indices on the same network.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

Hage, P. and Harary, F. (1995). ``Eccentricity and Centrality in Networks.'' Social Networks, 17:57-63.

### See Also

`centralization`

### Examples

    g<-rgraph(10)     #Draw a random graph with 10 members
    graphcent(g)    #Compute centrality scores

[Package sna version 1.1 Index]