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## [igraph] Assortativity function for R

 From: Tom Hebbron Subject: [igraph] Assortativity function for R Date: Wed, 25 Aug 2010 19:01:28 +0100

```Hi list,

I wonder if anyone can tell me why the assortativity code found on the
wiki at http://igraph.wikidot.com/r-recipes#toc7 gives different
results to simply passing the degrees of the edges directly to the R
cor function and selecting pearson correlation?

Looking back at Newman's paper
(http://arxiv.org/PS_cache/cond-mat/pdf/0205/0205405v1.pdf), it's
quite clear that the assortativity is equivalent to the Pearson
correlation coefficient of the degree at either ends of an edge. I can
also see that the provided R assortativity function from the igraph
wiki is a sound implementation of equation (4) from the paper.

#from igraph wiki http://igraph.wikidot.com/r-recipes#toc7
assortativity <- function(graph)
{
deg <- degree(graph)
deg.sq <- deg^2
m <- ecount(graph)
num1 <- 0; num2 <- 0; den <- 0
edges <- get.edgelist(graph, names=FALSE)+1
num1 <- sum(deg[edges[,1]] * deg[edges[,2]]) / m
num2 <- (sum(deg[edges[,1]] + deg[edges[,2]]) / (2 * m))^2
den <- sum(deg.sq[edges[,1]] + deg.sq[edges[,2]]) / (2 * m)
return((num1-num2)/(den-num2))
}

assortativity_b <- function(graph)
{
deg <- degree(graph)
edges <- get.edgelist(graph, names=FALSE)+1
return(cor(deg[edges[,1]],deg[edges[,2]], method="pearson"))
}

#test with, e.g.:

rg = erdos.renyi.game(40, p=0.2, directed=TRUE)
assortativity(rg)
assortativity_b(rg)

I get different values (in this case,  -0.05837817 and  -0.9867207)

Can anyone point out the problem here?

Thanks,
Tom.

```

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