User Tools

Site Tools


algorithms:katz

Katz Centrality

It is a centrality measure similar to Eigenvector Centrality, but solves the zero problem of that measure by assigning a small amount of centrality to each node. This amount is controlled by an external parameter called alpha. If it is very small, all nodes have the same centrality. As we increase alpha, nodes acquire centrality in a similar way as in the eigenvector centrality. Mathematically, the amount of centrality given to each node is with the largest eigenvalue of the adjacency matrix. Link weights may be considered. All Katz centrality values are normalized to a maximum value of 1.

Input parameter Type Default Description
Iterations* int > 0 100 Number of iterations in the plugin.
Alpha* float ∈ (0,1) 0.5 Amount of centrality assigned to each node. This number multiplies the reciprocal of the largest eigenvalue of the adjacency matrix in the computation.
Eigenvector property text None Node property that represents the Eigenvector Centrality. It speeds up the calculation. If not specified, BeGraph calculates it because it is required for the Katz Centrality in an intermediate step.
Weight property text None Name of the link property to use as a weight. Must have positive values.

* Required Field


In the case of a directed network, the Katz Centrlaity calculation may present numerical instabilities and give an error, in a similar way as the Eigenvector Centrality.

The next picture show the Katz Centrality for a social network. We indicate the most important nodes according to the Katz Centrality.



References:

  • M.E.J. Newman, Networks, an introduction, Oxford University Press, 2010, ISBN: 978-0-19-920665-0, sec. 7.3.
algorithms/katz.txt · Last modified: 2018/12/20 14:20 by systems