Hubbell Index



Where E is some exogeneous input and W is a weight matrix derived from the adjancancy matrix A. [HUBBELL, C. H. 1965]

This centrality value is defined by means of a weighted and loop allowed network. The weighted adjacency matrix W of a network G is asymmetric and contains real-valued weights for each edge.
where W = (wij) is the n×n adjacency matrix of the network. The column vector CH is the pattern of status scores (s1, s2, . . . , sn), and the column vector E is the pattern of exogenous inputs (e1, e2, . . . , en). The latter are often referred to as the boundary conditions of the system. If the boundary condition is unknown, E = Hubbell Index may be used. The solution CH of the above equation is termed Hubbell centrality or the Hubbell Index. [ZHANG, A. 2009]


Require connected and loop free network.


  • HUBBELL, C. H. 1965. An input-output approach to clique identification. Sociometry, 377-399.
  • JUNKER, B. H., KOSCHÜTZKI, D. & SCHREIBER, F. 2006. Exploration of biological network centralities with CentiBiN. BMC bioinformatics, 7, 219.
  • ZHANG, A. 2009. Protein Interaction Networks: Computational Analysis, Cambridge University Press.


HI, thank you for sharing all these good stuffs.  

When I calculate Hubbell index for a 176*176 weighted and directed nework, I have a following error message'

"Error in ev > 1 : invalid comparison with complex values". Could you tell me what this means?

Thnak you in advance


Add Replay written September 21, 2019, 5:56 am by Joon Jun

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