The results igraph R's closeness() and centralization.closeness()$res are different. It appears closeness() uses the sum of shortest path lengths whereas centralization.closeness() uses the average (before the inversion). Was this intentional? If so, it should probably be in the documentation. Also, the documentation is confusing. It states the function employs the average length of shortest paths (which is what centralization.closeness() uses) but the formula does not reflect this (but closeness() is consistent with formula).
This was found under igraph_0.6.5-2 (I haven't upgraded my R yet so I don't know if this was fixed in igraph_0.6.6 but the README doesn't report any of this).
Thanks.
Jay