# Bipartivity

#### Definition

The contribution of node

*i*to network bipartivity, β (*i*), can be obtained by using the subgraph centrality of node*i*: where (v_{1}, v_{2}, ..., v_{n}) is an orthonormal basis of R_{N}composed by eigenvectors of the adjacency matrix associated with the eigenvalues λ_{1}, λ_{2}, ..., λ_{n}, and v_{j}(i) is the ith component of v_{j}. Hence, β(i) is given by:**Note:**The values of β are confined to the interval [0.5, 1]. According to [ESTRADA, E. 2006], lethal proteins tend to have a low bipartivity score. Therefore you must adjust the value by setting it to 1 − β(i), such that lethal proteins potentially have a higher score.#### Software

#### References

- ESTRADA, E. & RODRÍGUEZ-VELÁZQUEZ, J. A. 2005. Spectral measures of bipartivity in complex networks. Physical Review E, 72, 046105. DOI: 10.1103/PhysRevE.72.046105
- ESTRADA, E. 2006. Protein Bipartivity and Essentiality in the Yeast Protein−Protein Interaction Network. Journal of Proteome Research, 5, 2177-2184. DOI: 10.1021/pr060106e