Thanks a lot Tamas, that makes sense in the end. If I have any bright ideas (doubtful...) for graph-level centrality measures for weighted graphs, will send them on!
Best, A ________________________________ From: igraph-help <[email protected]> on behalf of Tamas Nepusz <[email protected]> Sent: Friday, December 30, 2016 9:23 AM To: Help for igraph users Subject: Re: [igraph] Graph-level weighted degree, betweeeness, closeness? However, is the weight edge attribute of the graph automatically detected when calculating the graph-level versions of these three metrics? I guess not because the output seems to be blissfully ignorant of weights: > g <- make_ring(10) > centr_betw(g) $res [1] 8 8 8 8 8 8 8 8 8 8 $centralization [1] 0 $theoretical_max [1] 324 > E(g)$weight <- c(100, rep(1, 9)) > centr_betw(g) $res [1] 8 8 8 8 8 8 8 8 8 8 $centralization [1] 0 $theoretical_max [1] 324 I think the reason is that the graph-level cenrality metrics require the "theoretical maximum" of the centrality score across all possible connected networks with the same node count, and this is not well-defined for weighted graphs (because we don't know what we shall do with the weight -- shall we consider all possible permutations of the original weight set, or shall we consider weights uniformly distributed within a certain bounded or unbounded range?). If you can come up with or show us a formal definition of the centralization (i.e. graph-level centrality) score for weighted graphs, maybe we can come up with a solution using igraph. T.
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