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.
gcor(dat, dat2=NULL, g1=NULL, g2=NULL, diag=FALSE, mode="digraph")dat reflecting the first set of graphs to be compared; by default, all members of dat are included. dat (or dat2, if applicable) reflecting the second set of graphs to be compared; by default, all members of dat are included. diag is FALSE by default. mode is set to "digraph" by default. The (product moment) graph correlation between labeled graphs G and H is given by $$cor(G,H) = \frac{cov(G,H)}{\sqrt{cov(G,G) cov(H,H)}} $$ where the graph covariance is defined as $$cov(G,H) = \frac{1}{{|V| \choose 2}} \sum_{\{i,j\}} \left(A^G_{ij}-\mu_G\right)\left(A^H_{ij}-\mu_H\right)$$ (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.
Krackhardt, D. (1987). ``QAP Partialling as a Test of Spuriousness.'' Social Networks, 9, 171-86
gscor, gcov, gscov #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)
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