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NC  Normalized αCentralityDefinition
Bonacich defined αcentrality C_{i,j}(α,β,n) as the
total number of attenuated paths between nodes i and j, with β and α giving the attenuation factors along
direct edges (from i) and indirect edges (from interme
diate nodes) in the path from i to j, respectively, and n
is the length of the longest path. Given the adjacency
matrix of the network A, αcentrality matrix is defined
as follows:
Normalized αcentrality defined as matrix as:
Just like the original αcentrality, normalized αcentrality contains a tunable parameter
α that sets the length scale of interactions. For
α = 0, (normalized) αcentrality takes into account direct edges only. As
α increases, NC(α,β,n → ∞) becomes a more global
measure, taking into account ever larger network components.
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