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## [igraph] Reciprocity function

 From: Prof. Katharina Anna Zweig Subject: [igraph] Reciprocity function Date: Mon, 29 Jul 2013 16:08:38 +0200 User-agent: Mozilla/5.0 (Windows NT 6.1; rv:17.0) Gecko/20130620 Thunderbird/17.0.7

```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)
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

```