[igraph] Reciprocity function

[Prof. Katharina Anna Zweig]

Dear all,

for a book on network analysis I am currently looking into igraph's 
function reciprocity (in R, igraph_0.6-2). The documentation states that 
it is suitable for directed graphs:

http://igraph.sourceforge.net/doc/R/reciprocity.html

For fun, I used it on a directed and weighted graph:

require(igraph)
mat <- matrix(c(0,1,0,2,0,2,1,0,0), 3,3)
graph <- graph.adjacency(mat)
reciprocity(graph)

which yields 1/3

However, as stated by the documentation, reciprocity should do the 
following:

sum(mat*t(mat))/sum(mat)

which would yield 2/3.

I then thought igraph might be internally threshold the graph before 
using the reciprocity-function, so I tried:

graph2 <- simplify(graph)
reciprocity(graph2)

which yields 1/2.

From a theoretical standpoint, I think that the above formula for 
reciprocity should not be applicable to a weighted graph as it would be 
very difficult to actually understand what is measured there. Anyway, it 
seems that behind the curtains, the formula is not applied, at least not 
to the weighted adjacency matrix. Can you help me to understand what is 
actually computed?

Best regards,
Katharina Zweig


--
Prof. Dr. Katharina A. Zweig
Complex Network Analysis and Graph Theory
Computer Science Department
University of Science and Technology
Kaiserslautern
Gottlieb-Daimler-Str. 48/672
67663 Kaiserslautern
Germany

Telephone: +49 631 205 3346

www.ninasnet.de