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[igraph] Calculating average shortest path

From: Claudia Muller-Birn
Subject: [igraph] Calculating average shortest path
Date: Sat, 5 Mar 2011 23:53:14 +0100

Dear all,

I have a rather simple question regarding calculating the average shortest path 
length. There are actually to ways calculating it and I am wondering why I get 
two different results. Here is my toy example:

>  g1 <- graph( c( 0,1, 1,2, 2,1, 2,3 ), directed=FALSE )
>  g2 <- graph( c( 0,1, 1,2, 2,1, 2,3 ), directed=TRUE )

First possibility to calculate the average shortest path (or is it just one 
> average.path.length(g1, directed=FALSE)
[1] 1.666667
> average.path.length(g2, directed=TRUE)
[1] 1.571429

Second possibility would be by just calling the mean
> sp1 <- shortest.paths(g1)
> mean(sp1,na.rm=TRUE)
[1] 1.25
> sp2 <- shortest.paths(g2, v=V(g2), mode='out')
> sp2[is.infinite(sp2)]<-NA
> mean(sp2,na.rm=TRUE)
[1] 1

In my opinion, the second way to calculate the average shortest paths makes 
much more sense but then I am wondering about the meaning and calculation of 
the first possibility based on average.path.length. How is the latter function 
implemented or do I miss some settings?

Thank you very much for any help or idea.


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