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[igraph] Local measure of reciprocity in direct graph


From: capitano . nemo
Subject: [igraph] Local measure of reciprocity in direct graph
Date: Tue, 15 Jul 2014 12:09:54 +1000
User-agent: autistici.org webmail

Hi,

I have a direct graph of interactions among internet users. I am looking for a statistic to capture the level of reciprocity/mutuality of each node.

In other words, in a graph g, the edges connected to a vertex v can be of three types: mutual, asymmetric x -> v or asymmetric v -> x. I can thing of two different statistics which could give you an idea of the "prestige" of the node:

out.reciprocity = sum(is.mutual(g, E(g)[from(V(g)[v]), na.rm = TRUE) / degree(g, E(g)[v], mode="out")

and

in.reciprocity = sum(is.mutual(g, E(g)[to(V(g)[v]), na.rm = TRUE) / degree(g, E(g)[v], mode="in")

Would make sense to combine these two (in.reciprocity/out.reciprocity) to obtain a measure of node "prestige"?

Is there exist any other function that will do a better job?

Thanks

Francesco



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