NC - Normalized α-Centrality


Bonacich defined α-centrality Ci,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, α-centrality matrix is defined as follows:
NC – Normalized α-Centrality
Normalized α-centrality defined as matrix as:
NC – Normalized α-Centrality
Just like the original α-centrality, normalized α-centrality contains a tunable parameter α that sets the length scale of interactions. For α = 0, (normalized) α-centrality 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.



  • GHOSH, R. & LERMAN, K. 2011. Parameterized centrality metric for network analysis. Physical Review E, 83, 066118.


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