Re: [igraph] graph density on bipartite networks

[Gábor Csárdi]

Hi Simone,

On Mon, Oct 25, 2010 at 9:56 PM, Simone Gabbriellini
<address@hidden> wrote:
> 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"
>
> What do you think about this? I guess density for bipartite graph should be 
> 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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-- 
Gabor Csardi <address@hidden>     UNIL DGM