# centralgraph: Find the Central Graph of a Labeled Graph Stack In sna: Tools for Social Network Analysis

 centralgraph R Documentation

## Find the Central Graph of a Labeled Graph Stack

### Description

Returns the central graph of a set of labeled graphs, i.e. that graph in which i->j iff i->j in >=50% of the graphs within the set. If `normalize==TRUE`, then the value of the i,jth edge is given as the proportion of graphs in which i->j.

### Usage

```centralgraph(dat, normalize=FALSE)
```

### Arguments

 `dat` one or more input graphs. `normalize` boolean indicating whether the results should be normalized. The result of this is the "mean matrix". By default, `normalize==FALSE`.

### Details

The central graph of a set of graphs S is that graph C which minimizes the sum of Hamming distances between C and G in S. As such, it turns out (for the dichotomous case, at least), to be analogous to both the mean and median for sets of graphs. The central graph is useful in a variety of contexts; see the references below for more details.

### Value

A matrix containing the central graph (or mean matrix)

### Note

0.5 is used as the cutoff value regardless of whether or not the data is dichotomous (as is tacitly assumed). The routine is unaffected by data type when `normalize==TRUE`.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

Banks, D.L., and Carley, K.M. (1994). “Metric Inference for Social Networks.” Journal of Classification, 11(1), 121-49.

`hdist`

### Examples

```#Generate some random graphs
dat<-rgraph(10,5)
#Find the central graph
cg<-centralgraph(dat)
#Plot the central graph
gplot(cg)
#Now, look at the mean matrix
cg<-centralgraph(dat,normalize=TRUE)
print(cg)
```

sna documentation built on June 1, 2022, 9:06 a.m.