Hubbell Index

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 real-valued weights for each edge.

where W = (w_ij) is the n×n adjacency matrix of the network. The column vector C_H 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 = may be used. The solution C_H of the above equation is termed Hubbell centrality or the Hubbell Index. [ZHANG, A. 2009]

Require connected and loop free network.

• CentiBiN
  http://centibin.ipk-gatersleben.de/
• CentiLib
  http://centilib.ipk-gatersleben.de/

• 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.