Wishlist: Katz centrality and alpha centrality

[szhorvat]

What is the feature or improvement you would like to see?

Implement Katz centrality. This requires some linear algebra, ideally done with sparse matrices for good performance. The implementation will likely need to use CXSparse.

Use cases for the feature

This may be the most popular centrality measure not yet implemented in igraph.

References

• https://en.wikipedia.org/wiki/Katz_centrality
• Katz, Leo (Mar. 1953). “A new status index derived from sociometric analysis”. en. In: Psychometrika 18.1, pp. 39–43. ISSN: 1860-0980. DOI: 10.1007/BF02289026. URL: https://doi.org/10.1007/BF02289026
• Bonacich, Phillip and Paulette Lloyd (July 2001). “Eigenvector-like measures of centrality for asymmetric relations”. en. In: Social Networks 23.3, pp. 191–201. ISSN: 03788733. DOI: 10.1016/S0378-8733(01)00038-7. URL: https://linkinghub.elsevier.com/retrieve/pii/S0378873301000387

Related

• alpha_centrality() in the R interface is related

[ntamas]

Are alpha centrality and Katz centrality the same thing under different names?

Judging from the code in the R interface, alpha centrality would require inverting a sparse matrix only. cs_lsolve() or one of the related functions would probably be enough.

[szhorvat]

Are alpha centrality and Katz centrality the same thing under different names?

No, but they are closely related and it makes sense to implement them at the same time.

Judging from the code in the R interface, alpha centrality would require inverting a sparse matrix only. cs_lsolve() or one of the related functions would probably be enough.

Yes, these are easy to implement in any language that has sparse linear algebra support.