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
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