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Re: [igraph] graph density on bipartite networks

 From: Gábor Csárdi Subject: Re: [igraph] graph density on bipartite networks Date: Tue, 26 Oct 2010 09:40:58 +0200

```Hi Simone,

On Mon, Oct 25, 2010 at 9:56 PM, Simone Gabbriellini
> Hello List,
>
> I've found a possible issue in igraph regarding density for bipartite
> networks. According to this paper:
>
> Borgatti, S. P. and Everett, M. G. (1997). Network Analysis of 2-mode Data.
> Social Networks, 19(3):243–269.
>
> "the standard denominators are clearly not appropriate for 2-mode data, since
> no ties are possible within vertex sets. The maximum number of ties possible
> occurs when every vertex in one set is connected to every vertex in the
> other. If the vertex sets are of size ni and no then this amounts to ni*no
> edges in the undirected case and 2*ni*no in the directed case"
>
> calculated according to something like:
>
> ecount(g) / length(V(g)[type==FALSE]) * length(V(g)[type==TRUE])

yes, except that some parens are misssing. I think you want

ecount(g) / (length(V(g)[type==FALSE]) * length(V(g)[type==TRUE]))

Here is a function that works for directed networks as well:

density.bipartite <- function(graph) {
if (is.directed(graph)) {
ecount(graph) / sum(V(graph)\$type) / sum(!V(graph)\$type) / 2.0
} else {
ecount(graph) / sum(V(graph)\$type) / sum(!V(graph)\$type)
}
}

Best,
Gabor

> best,
> Simone
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