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 realvalued weights for each edge.
Hubbell Index
Definition
 C_{hubbell}=E+WC_{hubbell}
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 realvalued weights for each edge.
Requirements
Require connected and loop free network.
References
 HUBBELL, C. H. 1965. An inputoutput approach to clique identification. Sociometry, 377399.
 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.
Comments
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 Joon 

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