Re: [igraph] Graph-level weighted degree, betweeeness, closeness?

[Tamas Nepusz]

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.