Re: [igraph] degree centrality in 2-mode network

[Stefan Wallaschek]

Hi,

thank you Tamas for your response. The bipartite graph that I am using is not directed.

If I understand your answer correctly on how to calculate density, then, the code above might be wrong, because it says

# Number of top and bottom nodes
top<-length(V(g)[type==FALSE])
bottom<-length(V(g)[type==TRUE])
# Number of edges
m<-ecount(g)
# Mean degree for top and bottom nodes
ktop<-m/top
kbottom<-m/bottom
# Density for bipartite network
bidens<-m/(top*bottom)

So, it takes the actual existing number of edges in the bipartite graph and divides it by the product of the number of nodes for each type. Based on your described ratio, it seems to miss the total number of possible edges between the top and bottom vertices, right?
In my case and as an example, we have 11 "top" vertices and 17 "bottom" vertices and the number of edges (m) is 215 (because in this graph, there can be multipe edges between a top and a bottom vertice). If I take the numbers and calculate the density in the following way 215/(11*17), I get 1.15.

So, is there anything missing in the calculation or could the multiple edges in the network be the problem here? And how could it be solved?

Best wishes,
  Stefan

Am 06.06.2017 um 20:34 schrieb Tamas Nepusz:

The suggested code works out and I also checked the named reference for
further information, but I couldn't find anything about the ratio of
bipartite network density. It either doesn't seem to be the 0-1 ratio of
one-mode networks or I did something wrong, because I get results about
1.0 for the 2-mode-networks?

You are probably doing something wrong because the measure should be between 0 and 1. It is actually simply the ratio of the total number of edges and the total number of _possible_ edges between the "top" and the "bottom" vertices. If you get a result close to 1.0, it means that almost all of the possible edges between the top and the bottom vertices are present -- assuming that there are no edges between top-top or bottom-bottom, which should be the case anyway if it is a bipartite network.

One possible catch is if your network is directed; in that case, you should multiply the denominator of the fraction (i.e. the number of possible edges) by 2.

T.

_______________________________________________
igraph-help mailing list
address@hidden
https://lists.nongnu.org/mailman/listinfo/igraph-help

-- 
Stefan Wallaschek
Visting PhD fellow at School of Politics and International Relations (SPIRe)
University College Dublin
--
address@hidden
PhD Fellow
Bremen International Graduate School of Social Sciences (BIGSSS)/
University of Bremen
Mary-Somerville-Straße 9
P.O. Box 33 04 40
28359 Bremen (Germany)
https://www.bigsss-bremen.de/people/phd-fellows/stefan-wallaschek
Twitter: https://twitter.com/s_wallaschek