CODEWITHSUNDEEP
rigraph
eggfriedrice
eggfriedrice

Reputation: 27

How do you find betweennes centrality from igraph and what does the output number mean?

Hi so bascially lets say I have a network(A) and I want to find the betweeness centrality of it.

I used: centr_betw(graph, directed = FALSE, normalized = TRUE) This returned every node with the value:

[1] 1.827102e+04 3.554450e+04 5.000000e-01 9.524383e+04
[5] 0.000000e+00 0.000000e+00 1.078184e+05 4.768125e+04

I really want to know what these numbers mean.

It also shows the between centralization of the whole network and a max value. Lets say the network(A) as a whole has a betweenness centrality of 0.04. What can you say about this network(A) when it is compared to a random network with a betweeness centrality of 0.001?

MUCH THANKS GUYS

Upvotes: 1

Views: 376

Answers (1)

Julius Vainora
Julius Vainora

Reputation: 48251

Quite a bit of information can be found simply if you type ?centr_betw. In particular, centr_betw returns a list of three components: res, centralization, theoretical_max.

Each element of res is the betweenness centrality of a corresponding vertex i computed in this manner. Specifically, given a shortest path between some vertices j and k (not equal to i), i is considered to be more central if this shortest path includes i. Going over all possible pairs of j and k we can find this betweenness centrality of i.

Further, centralization and theoretical_max concern the Freeman centralization. centralization is C_x, which measures how central network's most central vertex is in relation to how central all the other vertices are. theoretical_max is the denominator of C_x providing the maximal possible value of the numerator across all networks with the same number of vertices.

So, if network A has Freeman centralization 0.04 and network B has 0.001, then we may say that the most central vertex of A is significantly more central than the most central vertex of B. If B is random (i.e., Erdos-Renyi), then that makes sense, because in a big enough network all vertices should play pretty similar role.

Upvotes: 1

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