[Jung-support] [jung - Open Discussion] Eigenvector Centrality Questions

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By: bdg146

I have some questions regarding JUNG's implementation of eigenvector
centrality.

According to some documentation I've found, the eigenvector centrality of Xi
is defined as the ith entry in the eigenvector corresponding to the largest
eigenvalue (as computed from the adjacency matrix).  This results in values
inconsistent with JUNG's output.

Eigenvector centrality also has the following property:

EigenvectorCentrality(Xi) = (1/λ) * sum(EigenvectorCentrality(neighbors_of_Xi)),
λ = the largest eigenvalue

This property holds true for the eigenvector implementation, but does not hold
true for JUNGs implementation.

For example, use the following undirected graph:

Nodes:
N1, N2, ..., N11

Edges:
(N1, N2)
(N1, N3)
(N1, N4)
(N1, N5)
(N1, N6)
(N1, N7)
(N1, N8)
(N8, N9)
(N8, N10)
(N8, N11)

According to JUNG, the eigenvector centrality of N1 is the equal to the eigenvector
centrality of N8.  The same does not hold true for the eigenvalue/vector
implementation.

What's going on here?  Am I misinterpreting something or using JUNG incorrectly?
Are there multiple interpretations of this metric?

Thanks for the help!

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