`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).

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

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.

ignore.eval

logical; should edge values be ignored when calculating geodesics?

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

The Harary graph centrality of a vertex v is equal to \(\frac{1}{\max_u d(v,u)}\), 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).

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

```
# NOT RUN {
g<-rgraph(10) #Draw a random graph with 10 members
graphcent(g) #Compute centrality scores
# }
```

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