[igraph] Incorrect theoretical max for betweenness calculation on large networks

[F Witmer]

I searched the archives and see some prior discussion regarding a problem with the betweenness calculation, but it looks like those issues were resolved.  When calculating the betweenness centralization, the theoretical max value appears to be incorrect causing nonsensical (negative) results.  Here's some R code and the results I get to reproduce it:

> library("igraph")

> g <- barabasi.game(5000)

> centralization.betweenness(g)$theoretical_max

[1] 345973414

> centralization.betweenness(g)$centralization

[1] 0.07282635

> g <- barabasi.game(10000)

> centralization.betweenness(g)$theoretical_max

[1] -1127329970

> centralization.betweenness(g)$centralization

[1] -0.02273176

And here's my session info:

> sessionInfo()

R version 2.15.2 (2012-10-26)

Platform: x86_64-w64-mingw32/x64 (64-bit)

locale:

[1] LC_COLLATE=English_United States.1252  LC_CTYPE=English_United States.1252   

[3] LC_MONETARY=English_United States.1252 LC_NUMERIC=C                          

[5] LC_TIME=English_United States.1252    

attached base packages:

[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:

[1] igraph_0.6-3

loaded via a namespace (and not attached):

[1] tools_2.15.2