gcor {sna} | R Documentation

## Find the (Product-Moment) Correlation Between Two or More Labeled Graphs

### Description

`gcor` finds the product-moment correlation between the adjacency matrices of graphs indicated by `g1` and `g2` in stack `dat` (or possibly `dat2`). Missing values are permitted.

### Usage

    gcor(dat, dat2=NULL, g1=NULL, g2=NULL, diag=FALSE, mode="digraph")

### Arguments

`dat` | one or more input graphs.
`dat2` | optionally, a second stack of graphs.
`g1` | the indices of `dat` reflecting the first set of graphs to be compared; by default, all members of `dat` are included.
`g2` | the indices or `dat` (or `dat2`, if applicable) reflecting the second set of graphs to be compared; by default, all members of `dat` are included.
`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.
`mode` | string indicating the type of graph being evaluated. "Digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. `mode` is set to "digraph" by default.

### Details

The (product moment) graph correlation between labeled graphs G and H is given by

cor(G,H) = cov(G,V)/sqrt(cov(G,G)cov(H,H))

where the graph covariance is defined as

cov(G,H) = sum( (A^G_ij-mu_G)(A^H_ij-mu_H), {i,j} )/Choose(|V|,2)

(with A^G being the adjacency matrix of G). The graph correlation/covariance is at the center of a number of graph comparison methods, including network variants of regression analysis, PCA, CCA, and the like.

Note that `gcor` computes only the correlation between uniquely labeled graphs. For the more general case, `gscor` is recommended.

### Value

A graph correlation matrix

### Note

The `gcor` routine is really just a front-end to the standard `cor` method; the primary value-added is the transparent vectorization of the input graphs (with intelligent handling of simple versus directed graphs, diagonals, etc.). As noted, the correlation coefficient returned is a standard Pearson's product-moment coefficient, and output should be interpreted accordingly. Classical null hypothesis testing procedures are not recommended for use with graph correlations; for nonparametric null hypothesis testing regarding graph correlations, see `cugtest` and `qaptest`. For multivariate correlations among graph sets, try `netcancor`.

### Author(s)

Carter T. Butts buttsc@uci.edu

### References

Butts, C.T., and Carley, K.M. (2001). ``Multivariate Methods for Interstructural Analysis.'' CASOS Working Paper, Carnegie Mellon University.

Krackhardt, D. (1987). ``QAP Partialling as a Test of Spuriousness.'' Social Networks, 9, 171-86

### See Also

`gscor`, `gcov`, `gscov`

### Examples

    #Generate two random graphs each of low, medium, and high density
    g<-rgraph(10,6,tprob=c(0.2,0.2,0.5,0.5,0.8,0.8))

    #Examine the correlation matrix
    gcor(g)

[Package sna version 1.1 Index]