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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
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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:


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

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

which yields 1/3

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


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)

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
Gottlieb-Daimler-Str. 48/672
67663 Kaiserslautern

Telephone: +49 631 205 3346


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